Spheroid Dropship

A Sci Fi plot calls for a vehicle that can land on an alien planet and be somewhat Badass. A Space Plane would be cool, but you'd need a runway. So instead, you have a Drop Ship shaped roughly like a sphere that consists of a vertically mounted rocket engine surrounded by landing struts, fuel, cargo, a control room, and usually a ramp to offload personnel and cargo. The type of engine is unimportant. It can be an actual rocket or a Handwaved "antigravity generator" or "reactionless thruster".

Why a sphere?

From an aerospace engineering perspective, there could be several good reasons:
- A sphere is the only shape that is aerodynamically identical in any direction, a fact that might be of interest to a Sufficiently Advanced Alien.
- A sphere, while doing away with wings that would be useless in space, is still more aerodynamic than, say, a cube. While it might not generate much lift, it could be quite maneuverable in both space and atmosphere.
- Spheres have been shown as an effective shape for atmospheric reentry, as demonstrated by the Soviet manned space program.
- Of all possible spacecraft shapes with the same internal volume, a sphere has the least surface area (which also means that of all possible spacecraft shapes with the same surface area, a sphere has the most internal volume.) This might make it a good choice for both commercial and military use, as it would store the most cargo per unit of armor.
Spheres are also naturally an extremely strong shape (this is why many deep sea submersibles are spherical) which would help in the harsh conditions of both space and many planets with a thick atmosphere.
More importantly to writers, spheres are cool.
- Spheres are "cute". consider this commercial.
- Spheres are sleek, but not as stereotypical as a Flying Saucer or Retro Rocket.
- Spheres are Badass. Nothing says "we mean business" like a Mother Ship that looks like a wrecking ball with guns.
- Perhaps most importantly of all, spheres are alien, but not too alien. We instantly recognize a sphere as a familiar shape, but not one we're used to seeing in the sky. They've got Sinister Geometry, but still clearly leave open the possibility we could find that their crews are Not So Different from us.

Requirements:

It must look like a spheroid. Obviously there will be some variations. Antennae, landing gear, square hatches, etc., are all fine as long as they don't detract from the fact that it's still basically a spheroid. Egg shapes and squished spheres are also OK as long as its closer to being a sphere than it is to a cylinder or Flying Saucer. However, examples that are arguably less a sphere than a "fat vertical rocket", "rotund Flying Saucer", "sphere on a pole", etc. should be listed elsewhere.
Vertical takeoff and landing. The vehicle is essentially incapable of landing like a traditional airplane. Once airborne, it can change course.
Single-stage, surface-to-space capability. Sufficiently Advanced Aliens usually equip such vessels with interstellar capability, while more primitive variants may only be capable of going between the planet and an orbiting Mother Ship.

Examples of Spheroid Dropship include:

Anime and Manga

Dragonball Z: Frieza's Saiyan Pods are of the sufficiently advanced variety.
A Wind Named Amnesia features an especially huge one.

Film

Sphere. Technically not a drop ship, but still an alien "spacecraft".
The alien spaceship in ET the Extraterrestrial.
The classic Aries trans-orbital shuttle that takes Heywood Floyd from Station V to the Moon in 2001: A Space Odyssey fits this to a T.
Starman may be the Trope Codifier, as seen in the Trope Image.
The alien "Gods" in Puma Man is also a round sphere.
The Lucrehulk-class Core Ship in Star Wars II: Attack of the Clones are dual purpose ships. They're the central "command" core of the Trade Federation ships, but can also detach to serve as landing craft, or fly independently.
The Borg Sphere in Star Trek: First Contact hovers somewhere in the gray area between trope played straight and subversion.
- It's definitely a spheroid, and the only reason it's not a dropship is because Enterprise destroyed it first.
The Remake of The Day the Earth Stood Still has a spheroid energy vessel of some sort, instead of the classic Flying Saucer that landed on the Mall in the original.
The Hitchhikers Guide to The Galaxy movie has ~~a ball~~ tons of fun with this trope.
The spaceship in Attack of the 50 Foot Woman, except the characters call it a satellite because the screenwriter Did Not Do the Research. (It was made when Sputnik had just made 'satellite' the latest buzzword. The 1993 remake uses a straight-up Flying Saucer.)
The lifepod in Starship Troopers 3: Marauder.

Films - Animated

The second Katy Caterpillar movie, Katy, Kiki & Koko had the shapeshifting alien use such a ship. It was not capable of taking off vertically and had to reach escape velocity by bouncing on the ground.

Literature

The derelict space craft from Andre Norton's Time Traders series were giant spheres. In the second book, Galactic Derelict, the heroes managed to find one intact.
In Magnus, Dragylon the Imperial Fortress is a massive, invisible, sun-sphere and headquarters of Lucifer. Dragylon also contains the Library of Babel and Lucifer's Cool Chair.
In The Black Fleet Crisis, the Yevetha's thrustships are spherical, based on the surface area argument quoted above. Probably the only Star Wars example that isn't somehow related to the Death Star.
The sphere is a reasonably common shape for starships in Perry Rhodan. Most notably, it's been traditionally used by the dominant humanoid races of the Milky Way galaxy, the Terrans themselves included, for their capital ships (basically anything above fighter/small craft scale) for thousands of years, so there are plenty to go around.
E.E. Smith favoured this shape in the Skylark universe (only Skylark Three was elongated) and for the FTL capital ships in the early part of the Lensman sequence. By the time of First Lensman, however, the teardrop shape is becoming more prominent and the spheres are having trouble keeping up (literally). After the first space battle in that book, no more spheres are built and it's implied the ones which exist are phased out. By Kim Kinnison's era the ships are all teardrops.
Peter F. Hamilton's famous Night's Dawn trilogy features a lot of spherical spacecraft (e. g. The Lady Macbeth), due to the FTL drives creating a spherical area for the travel - anything poking out is cut off. They are mostly used by the Adamists, one of the two major factions of future humanity in that series. While they are never shown to land on planets (instead preferring to ferry freight using a Space Plane), they could presumably land on a planet vertically due to their huge fusion engines and fuel tanks.
In H. Beam Piper's Terro-Human Future History, especially seen in Space Viking, where the protagonist commands a 2000-foot across globe with a huge skull-impaled-on-a-sword insignia painted on. (Some cover pictures made it a "sphere on a pole," but this is a mistake.) The artificial gravity generator is at the center, and a few passages seem to indicate that the gravity radiates from the center -- although this would cause problems if it ever shut down while the ship was on a planet surface, so that "down" wasn't toward the ship's center any longer....

Tabletop Games

The trope was named for Spheroid Dropships in BattleTech. See here for an example design. Note the Humongous Mecha on the lower right.
The Broadsword class mercenary cruiser in Traveller. Oddly, though its description says it can't land on planets with atmospheres, one does exactly that in Adventure 7 Broadsword.

Video Games

These are present in the Mechwarrior and Mech Assault game series, which is based on BattleTech.