Sci-Fi Writers Have No Sense of Scale/No Sense of Velocity

Anime and Manga

Space Cruiser Yamato has the Earth see the approach of the Comet Empire, even though it's light years away and the light from it wouldn't reach us yet. Also, the Comet Empire is the size of a small planet - big, but not big enough to be seen at that distance anyway.
- In the Americanization, Star Blazers, the newly launched Argo makes its first hyperspace jumps, traveling light years from Earth to Mars. Must have been a bit of a detour involved.
In Tengen Toppa Gurren Lagann, the final battle against the Anti-Spiral and the eponymous mech takes place on a scale so huge entire galaxies are visible in single shots, and any movement is far beyond light-speed. By that point in the series, physics have been ground to a fine powder.

Comic Books

Any time you are dealing with a speedster like The Flash, the laws of drama beat up the laws of physics and take their lunch money.
- The Flash's writers eventually gave up trying to apply science to the Scarlet Speedster, and introduced the magical Speed Force.

Films -- Live-Action

Starship Troopers (The Movie) once again shines through with a huge asteroid passing a battleship vastly distant from Earth, with the same asteroid striking the Earth mere hours later. To add insult to injury, the battleship was also moving towards the asteroid, yet the asteroid seems to slowly pass by happily ripping off a section of the ship as it does so - suggesting the ship is, in fact, flying backwards at a velocity very close to but slightly slower than the asteroid.
- Might be handwaved by saying that interstellar travel in this universe works by distorting space around the travelling object such that lightyears are compressed to kilometers. Then speeds of a few km/h would be sufficient...
Parodied in Spaceballs:

Colonel Sandurz: Prepare ship for light speed.
Dark Helmet: No, no, no. Light speed is too slow!
Colonel Sandurz: Light speed too slow?
Dark Helmet: Yes. We're going to have to go right to...ludicrous speed!
Colonel Sandurz: Ludicrous speed? Sir, we've never gone that fast before...I don't know if the ship can take it.
Dark Helmet: What's the matter, Colonel Sandurz? Chicken?

In just every work involving an Asteroid Thicket, spaceships are seen passing rocks at relative speeds that would be about right for seagoing vessels passing an island. If there is a chase inside this asteroid field, it looks like a downtown car chase (or jetplane chase, if you're generous). In reality, even with today's technology, flybys are measured in dozens of kilometers per second.
In Star Trek: The Motion Picture the Enterprise has left space dock and is on its way to intercept V'Ger. It heads away from Earth and, moving at only sublight speed, manages to pass Jupiter only a few moments after leaving Earth orbit.

Literature

Justified in Animorphs where travel through Zero Space is explicitly stated to be relatively random, where the same distance can take either hours or months, depending on how Zero Space shifted.
Stationery Voyagers has all Physicalia settings happen in the Inktacto star system, with only six worlds "a few moons' distance" away from each other, and held in place by the Muellex so they won't crash into each other. Far from talking about astronomical units, let alone lightyears and lightspeed, characters travel distances in speeds described as Mach numbers. These, in turn, are defined as Mach 1 = 700 Mornots per hour (742 miles per hour), to get around the fact that a relation to the speed of sound would otherwise be meaningless in space. The entire premise holds together only because, with the exception of the frozen wasteland world of Menehune and the Muellex-engulfed-yet-oxygenated world of Haragad, all planets are ~~Earth~~ Mantith-like.
In Tunnel in the Sky, two teenagers notice a new visible star above the alien world they're stranded on, and conclude that they've just witnessed a nova. At the book's end, it's revealed a nova is what interfered with their Cool Gate back to Earth. If it's the same nova -- which is strongly implied; indeed, the chapter where they see it is titled "The Nova", and it reads like a Chekhov's Gun -- then the boys shouldn't have been able to see its light until years after it happened.
Overlapping with Distance, there's an essay out there that analyzes the Threadfighting tactics in the Dragonriders of Pern stories. It concludes that in order for the tactics described to work against the Threadfall patterns described, either the dragons must be flying at barely-subsonic velocities, Thread is drifting downward somewhat slower than a falling leaf, or the dragons are emitting gouts of flame better than half a mile long.

Live Action TV

The USS Enterprise in Star Trek: The Original Series traveled to the edge of the galaxy (in "Where No Man Has Gone Before" and "By Any Other Name") and to the center of the galaxy (in Star Trek V the Final Frontier) in the space of a single episode. The trip from one galaxy to another would take about 300 years (though the trip would be made with the modifications of extra-galactic aliens who had engines that were better than the Federation's). Yet in Star Trek: Voyager, when ships were about a thousand times faster, the estimated travel time to Earth from the opposite side of the galaxy was upwards of 70 years.
- Several episodes of original Trek have the Enterprise departing the planet-of-the-week at Warp Factor 1. This would mean they're travelling at the speed of light. At that rate, it would take them years just to get to the nearest neighboring star system. (Perhaps Kirk cranks it up to warp 6 once they're past the asteropause.)
By the time of Star Trek: The Next Generation, a Warp Speed scale was firmly established by Paramount, where a speed of Warp X (below Warp 9) meant the ship was travelling at X^3.3333... times the speed of light. This makes Warp 1 equal to light speed, Warp 2 just a hair over 10 times the speed of light, and Warp 9 a little more than 1500 times light speed. Yet in the episode "Where Silence Has Lease", the Enterprise traverses the 1.3 parsec distance to the edge of a giant space cloud at Warp 2 in about 30 seconds.
- Which fits with the Voyager example, which has the cruising speed of the ship at about 1,000 times the speed of light.
- ...and which was completely abandoned by Deep Space Nine, where travelling pretty much anywhere invariably took about half a day. Runabouts (established as having a top speed of warp five) seemed to be able to reach Earth, Cardassia, and various other locations in the same short amount of time (while the distances aren't given, that would put both the Federation and Cardassian capitals within two light years of each other at most). On another occasion, a runabout travels to a planet given as five light years away in a few hours (it should take over a week).
In Star Trek: Enterprise, the Klingon homeworld is several days' travel from Earth, which would put the two empires right on top of each other, given the increases in cruising speed in the other incarnations of the franchise. (Though one interesting exception: in the first episode of Star Trek: Enterprise, Trip describes the ship's top speed in terms of how long it would take to travel to Jupiter and back, and he's exactly right, based on conventional estimates of how warp factors work). In fact if you use those same calculations, the Klingon home planet would be two and a half lightyears from Earth; the nearest star to us in Real Life is four and a half. Missed it by that much. Which is, really, still a hell of a big distance in conventional terms, but isn't that much in terms of space.
In Star Trek: Voyager, it is stated, that the 70 000 light years back to earth even at maximum speed (Warp 9.975) would take 75 years, so that would make a maximum of 933 light years per year or just under 3 light years per day. Of course only if they always travel at full speed (which they don't). Yet in every scene where you can see a window, you can see hundreds of stars passing by in a mere seconds. Never mind, that stars are usually light years apart).
- Star Trek: The Motion Picture started the tradition of showing stars streaming past the window whenever they were at warp speed. Even at the movie-Enterprise's maximum safe cruising speed of warp 6 (TOS scale), they'd still only be going 216 times the speed of light, too slow for distant stars zip past in a matter of seconds as shown. Some fans explains that these aren't stars but dust particles that interact with the warp field.
- Getting back to Voyager, not surprisingly, the most ridiculous example in the other direction is the episode "Threshold", where Tom Paris briefly pushes a shuttle to "infinite velocity"(!) Not only is everyone on the ship shocked when the shuttle gets out of range of Voyager's sensors in seconds, but the shuttle's sensors only detect information from the sector. Later he does it again, this time trying to get as far from Voyager as possible, and he winds up parking on a planet that Voyager can reach at its usual speeds in three days.
- Even ignoring "Threshold," Voyager is guilty of contradicting its own warp speed scale. Although Voyager's top speed is supposed to be Warp 9.975, in the episode "The 37s" it's stated that warp 9.9 is about 4 billion miles per second, which works out to 21,473 times the speed of light. At that speed -- which is lower than their own cruising speed -- they could cross the 70,000 light years back to the Alpha Quadrant in a little over 3 years, unless warp 9.9 can't be done for years on end, the way warp 6 seems to be able to.
  - Confirmed in cannon, most ships can only travel at there top speeds for 12 hours.
Space: 1999 comes through again by having characters track the approach of faster-than-light craft optically, and by allowing floating space rubble, conventional rockets, alien spacecraft, and a moon hurtling interstellar distances in days to be in range of each other for exactly as long as the plot demands.
In Babylon 5 hyperspace travel appears to be done at the speed of plot. For example, it takes 3 days to get from Babylon 5 to Earth, which is about 14 light-years away. It also takes 3 days to get from Babylon 5 to Z'ha'dum, which is about 20,000 light-years away. In fairness the creator readily falls back on the "It's hyperspace!" argument every time anyone even starts to talk about this.
- In fact, in the DVD commentaries he explicitly says that the White Star "moves at the speed of plot".
Stargate SG-1 and Stargate Atlantis zig zag this trope. One the one hand, the Daedalus is able to reach Atlantis for the first season finale in about three days while powered by a ZPM. The Pegasus Galaxy (assuming the one in the series is the Pegasus Irregular Dwarf Galaxy in Real Life as is implied) is 3 million lightyears from the Milky Way. That's a speed 365 million times the speed of light. It's also mentioned that the trip would take about 2 weeks without the ZPM. That's about 78 million times the speed of light. Taken by themselves, these don't seem horrifically unreasonable. The universe runs on MORE POWER!. The problem comes when one considers that it usually takes them a few days to get any where in the galaxy. At the aforementioned speeds, they could traverse the entire observable universe in and 55 and 255 years, respectively. So either they normally run their engines far below their capacity, or it's this trope.
- At one point it was explicitly stated that ships had separate drives for interstellar and intergalactic travel, for whatever reason.

Tabletop Games

Handwaved in Warhammer 40,000, where the chaotic nature of the Warp means that the same trip can take vastly different amounts of time. We have at least one example of a ship arriving quite some time before it left, and another of a vessel arriving at it's destination millennia after it was supposed to arrive, though the crew seemed to believe it took only a couple of months. When your hyperspace is made of illogical thought, it's no wonder there's a bit of variation in travel times.
- In one case this is used for some dark humor. A crew of a ship responding to a distress signal travels through the warp ending up being attacked by demons. They proceed to send out a distress signal... which is sent back in time due to the anomalies in the warp, the very signal that they themselves responded to.
- 40K also came up with a nice solution for the Necrons: the Inertialess Drive. It makes the ship unbound by inertia, allowing it to almost instantly (the time it takes for the drive to activate) accelerate to a practically infinite velocity, then immediately come to a stop. Necron phase technology would prevent them from crashing into anything, and the precision of their machinery (their weapons, for example, are crafted atom by atom, as an idea of how precise Necrons are) would ensure they don't go waaaay too far, out past the galaxy.

Video Games

In System Shock 2, it's discovered that a piece of the space station which was jettisoned by the player in the first game has crashed on a planet in the Tau Ceti system - crossing a distance of 12 light-years in a mere 30 years. This would require the ejection charges to have kicked the module loose at about half the speed of light...
- Then there's the issue about crashing the planet at half the speed of light...
Ratchet and Clank Future: A Crack In Time has the titular heroes caught by Dr. Nefarious and propelled off his space station on a catapult-like device to their assumed deaths. They awaken on a planet "hours later". A large catapult is not likely to propel anyone to fast enough speeds to reach a planet outside presumed detection range without turning them into paste. Also may qualify as a Distance example.
- When comparing the distances and sizes of moons and planets in Crack in Time, this makes considerable sense. In R&C, the planets and moons really are that close together.
Each individual map in X-Universe series is at most two hundred kilometers across, and as little as tens of kilometers in the original Beyond the Frontier -- almost comically small by astronomical standards -- yet your ship requires a Time Dilation device to travel between locations on the same map in a reasonable amount of time. Unless the kilometer was redefined at some point, this suggests spaceships in the game are far, far slower than they have any right to be -- raising the interesting question of how any of the spacefaring races actually managed to become spacefaring races when they don't seem to have any ships that come anywhere near escape velocity for a planet with a mass similar to Earth.
Star Ruler: You can travel faster than light on raw engine power alone, no Phlebotinum handwave provided. Lasers also remain hitscan even as their effective range becomes measurable in AU, which means that they are travelling FTL as well.

Western Animation

In The Magic School Bus episode "Out of this World", the class has to stop an asteroid from hitting the Earth, specifically their school. It takes the whole episode for the asteroid to get close to Earth and that's with Dorothy Ann having tracked it for days prior to the start of the episode. They defeat it by changing its trajectory to Hurl It Into the Sun, which it manages it hit within the span of a few seconds. This is Lampshaded in the producer segment ("Our show is less than thirty minutes long, what could we do?")

Other

Although this doesn't involve space ships, the roleplaying site Mega Man MUSH once had a memorable example of this in its news files for the various character stats, describing what the specific numbers for each stat would represent. In the news file for the Velocity stat, where 1 signified "less than 5 mph (8 km/h)", 5 meant "60-150 mph (97-241 km/h)", and 9 was specified as "767 mph (1235 km/h)" (the speed of sound), 10 was defined as "escape velocity". Hilarity ensued when someone pointed out exactly how fast escape velocity is.
- To those who aren't into reading through the math in that link, Escape Velocity is 11.2 km/s, or over 40,000 km/h, thus leaving a drastically large gap between ratings 9 and 10.

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