People in Rubber Suits

The original Man In A Rubber Suit, Haruo Nakajima.

"MAN IN SUIT! MAN IN SUIT! MAN IN SUIT!"

—Harry Knowles of Ain't It Cool News on (classic) Godzilla

The single most important special effect of all time, bar none; the man in rubber suit technique was Hollywood's original go-to method for portraying the extra-terrestrial invader, the experiment Gone Horribly Wrong, and the supernatural terror before computer generated effects were a twinkle in a programmer's eye. This is not to say that the method is perfect, many a great riff has been made at the expense of the weaker displays of this technique, but even at its lowest the man-in-suit still takes notoriety in the form of Narm Charm.

Note: Not necessarily made from rubber.

Compare Pantomime Animal.

Examples of People in Rubber Suits include:

Film

Played to great effect in Predator. The original Predator costume was a rather goofy and awkward lizard; the crew asked for a new monster design very shortly after seeing the original. The designer decided to try something with mandibles...
In the 1976 remake of King Kong, Jeff Bridges' character reacted to the plunderers' initial disbelief upon seeing the giant ape by saying "What do you think it was? A man in an ape suit?"... which is exactly what it looked like, because it was.
The film adaptation of Beowulf starring Christopher Lambert reimagined Grendel as a man in a rubber suit... with a clearly visible zipper (it also reimagined Grendel's mother as a Cute Monster Girl who would later prove to have flammable blood).
Star Wars: Original footage with Jabba the Hutt, who was actually a ludicrously complex puppet with two full-sized people inside his torso plus a midget in the tail and a team of offscreen operators for his eyes and facial expressions. Chewie and the Ewoks count as well.
Godzilla is an interesting case; Originally, Godzilla was to be animated in stop-motion, like The Beast from 20000 Fathoms. Eiji Tsuburaya informed the producers that the necessary scenes would take seven years to complete, so he was instead told to create the monster another way. He came up with a new plan: instead of splicing a tiny stop-motion model into live-action footage, make a realistic monster suit and build a set where everything is tiny compared to it. It worked.
- Applications of this method in the years after Tsuburaya's death in the Showa period turned out not to be as impressive, however... but they do have their charm.
Jurassic Park used men in (partial) suits for the Velociraptors in some shots. The raptor that walks to the fallen mercenary and plunges its claw into his back in the third film was a man wearing raptor pants.
Hyde (the Evil Twin of Dr. Jekyll) in The League of Extraordinary Gentlemen movie combines blue screen, forced perspective and a rubber suit so spectacularly obvious that, like much of the movie, it borders on Special Effect Failure. (And borders is a very generous term.)
- Your Mileage May Vary, both in regards to the suit and the movie. Hyde certainly looked better than the CGI Hulk, out the same summer.
Creature from the Black Lagoon One of the earliest (perhaps THE earliest) representation of Gill-men used this way.
The 1936 Flash Gordon serial may be the Ur Example champeen, as it featured a man in a suit portraying a giant dragon some 18 years before Toho lit upon the idea.
In the film The Bad and The Beautiful, a director and a producer are assigned to make a low-budget horror film about cat men, who are supposed to be played by people in crappy suits. They declare that "five men dressed like cats look like five men dressed like cats", and they make the film without showing the monsters (a reference to the real classic horror film Cat People).
The 1957 movie Night of the Demon, directed with dark understated dread by veteran Jacques Tourneur, from a story by horror master MR James, was considered by many to be undercut by Executive Meddling insistence on a rubber-suit demon (showing up at the beginning, no less).
Pearl (the grotesquely obese vampire) from Blade. It sounds like a grim kid's TV show.
The Rodents Of Unusual Size from The Princess Bride.
The Thing was played by a rubber-suited Michael Chiklis in the Fantastic Four movies.
The Xenomorph in Film/Alien and Aliens. They are MUCH scarier than most people in rubber suits though because they have such a un-human like head and body that its hard to tell yourself they're just men in suits. Even more so in the first movie, where the alien was played by a 7FT 2INCHS TALL, but slender...student.
The Hellboy series of movies (Both directed By Guillermo Del Toro) use this technique a lot, and to great effect. In fact, they almost always opt to minimize the use of CGI as much as possible. Granted though, their rubber suits are most often pretty damn advanced (containing heaps of animatronics and whatnot).
This technique was used for the Humongous Mecha sequences in the Tekkouki Mikazuki film series.
One early rubber-plus-animatronics example was 1959's The Alligator People, in which the transformed protagonist's final gator head had a working jaw. Still looked very fake, the moreso because he winds up interacting with an actual alligator.
In Night of the Lepus this is how the giant killer bunny rabbits are portrayed when they attack people. The suits...pretty much look nothing like giant bunnies.
Used in the film The Last Dinosaur, here.
Unknown Island from 1948 for the Ceratosaurs did this. The Ground sloth was also a suit, but mostly fur and rubber mask.
One Million B.C. has one rubber suit dinosaur amidst dozens of Slurpasaur dinosaurs.
Octaman (1971) Behold the horror.

Comic Books

In-Universe example in The Transformers. The Decepticon Skullgrin used his Pretender shell to become a star in monster films.

Live Action TV

Pretty Guardian Sailor Moon went through literally dozens of these as their Monsters Of The Week.
Kamen Rider is fond of people in rubber suits as well, though theirs tend to be a little more serious in comparison to Sentai.
- Justified in that a lot of the monsters are very intricately designed with a motif in mind and would be practically impossible to reasonably create without a lot of money. It should also be noted that the Heisei riders often have monsters that are CGI generated like Hibiki and Ryuki. This may have something to do with why recent series have had stories take place in two-part arcs - half the monster suits to make.
The Ultra Series thrives entirely on the design of ever more Crazyawesome rubber suits. This applies to both heroes and villains.
Madan Senki Ryukendo, however, creates oddities such as a monster best described as a flying mood ring laser elephant.
Doctor Who, too many times to mention. For his first-ever Doctor Who story (the second-ever for Doctor Who generally) Terry Nation invented the Daleks as a way to avert the People in Rubber Suits. They still had plungers for hands. His second story (the fourth aired on Doctor Who) however already featured the Voord, literally, People in Rubber Suits. (Possibly. Perhaps the suits have fused with their actual bodies.)
- At least once, in The Ark in Space, the monster was actually made out of green bubble wrap - but considering that bubble wrap had only just been invented, the overall effect worked, if only for about five years after the episode's premiere. Supposedly the bubbles went 'pop-pop-pop' as the extras inched their way across stage reducing cast and crew to hysterics and the sound department to tears.
- It's not limited to rubber suits, either - the Krotons from the eponymous Second Doctor serial resemble walking cardboard boxes with a (sometimes spinning) cardboard diamond on top.
- The Zarbi (First Doctor, The Web Planet): giant ants with two very, very humanoid legs.
- Scared of those new series Cybermen? The original Cybermen were guys in a balaclava and a (somewhat loose) catsuit, carrying plastic stuff suspenders-like. Plus a funnel on their heads. And a serious speech impediment. It actually worked; they were terrifying instead of being ridiculous.
The Sarah Jane Adventures. Like Doctor Who, except a smaller budget = less CGI + more people in rubber suits.
- Brilliantly lampshaded:

Chrissie: I’m telling you; my ex-husband is being chased by a dwarf in a suit- now I’ve seen it all!

Star Trek mostly has Rubber Forehead Aliens, but some (the Gorn, for instance) play this trope straight. "Arena" became one of the most iconic episodes because of this.
- As time went on those species that were once men in suits were replaced by Serkis Folk. The Gorn appearance in Enterprise was all CGI, for example.
Power Rangers, once a week from 1992 to the present day. Super Sentai, from 1975 to the present, with the same rubber suits.
- Lampshaded in an episode of Dino Thunder. The Power Trio were watching an episode of Abaranger (long story) when Connor complains that the Monster of the Week was obviously a man in a rubber suit. Kira just pointed out that it was no weirder than what they fought.
The Sleestaks from the Land of the Lost TV shows.
Legion from Red Dwarf.
The X-Files. Spoofed in "Jose Chung's From Outer Space". Scully begins performing an autopsy on a Grey Alien found dead in a field, only to find a zipper; it turns out to be a rubber suit. The video footage is edited and sold as a tape of an actual Alien Autopsy.
Andromeda, with all the Narm Charm, couldn't pass up this trope. Some Magog even have visible zippers.
Most of the dinosaurs in, well, Dinosaurs.
- The rest, however, are played by hand puppets.
The A-Team: In one episode, Hannibal is shown to be in a Godzilla costume as part of a job. Also seen in the opening credits, without the headpiece on while smoking one of his iconic cigars.
Spoofed in Danger 5 along with other Narm Charm cliches.

Western Animation

Done as a Show Within a Show segment on Doug. Doug and his friends watched a horror movie where you didn't see the shapeshifting killer monster (in his real form at least) until the end of the movie. Doug was so scared that he closed his eyes and missed the scene. He started to suffer from nightmares afterwards, and reasoned that sitting through the whole scene with open eyes would make them go away, so he kept trying to see it but always ended up wimping out, until the final time, where he managed to not only see the monster, but laugh as it was an obvious rubber suit with a clearly visible zipper. When he mentioned this to his friends they all admitted that they had closed their eyes too.
Lampshaded by the Duck Dodgers cartoon, with a Godzilla-like monster called "Maninsuit".
On The Flintstones, Fred got a job in a monster movie not as the monster, but as the stand-in for the actor playing the monster.
Oh the ghost is here, it's a crook in a suit.The ghost is here, he's protecting some loot.
Owen from Total Drama World Tour dressed up as Godzilla for his team's commercial in Japan.

Alejandro: Oh nooo, a large, out-of-shape monsteeeer!

Other

A very curious example is Dr. Dale Russel's "thought experiment", the Dinosauroid. Revised versions look even less humanoid.
Some very ambitious LARP players.
In every main-series iteration of Wing Commander after II, the Kilrathi. Series creator Chris Roberts was NEVER happy with their appearance.
The one-panel Newspaper Comic Bizarro once showed a newscaster announcing, "The city is being attacked by an enormous Japanese actor in a rubber suit!" and sure enough, it's recognizably Godzilla ravaging the background.
In an early music video ("Elephant Parts", 1981), Mike Nesmith is wearing the bottom half of a rubber suit while singing "Her Name Was Rodan".