The platformer version of space — which is basically like every other platformer stage, except that you might jump a little higher due to lessened gravity. It may take place in a space station, densely-packed asteroids or on an planet or moon surface where the atmosphere is missing.
Deep Space from Kingdom Hearts: Birth by Sleep, which is based on the prologue of Lilo & Stitch. Parts of the stage allow you to explore the areas outside of the spaceship and even allow you to turn off gravity to reach higher places in the spaceship.
Gradius, R-Type, and all their variants and spinoffs. Special mention to the Genesis title Whip Rush. Several levels feature segments where your titular starship flies up, down, and even backwards, all while obediently facing and shooting to the right. It requires getting either missile or flamethrower powerups to be able to shoot in the direction you're going.
The final stage of Wily's fortress in Mega Man 10, along with the fight against the Wily Capsule.
The seventh chapter of Disgaea 3: Absence of Justice takes place on a path that goes through outer space, and connects the game's netherworld with the human world (Which exist as separate planets, contrary to what the names may imply).
The space levels in Ratchet & Clank (at least in the first game) seem to avert this trope. Ratchet can't go out there himself, but has to send his Robot Buddy Clank to explore. Then it turns out that the only thing Ratchet needed was an oxygen mask, and suddenly the space levels function exactly as the planet levels. Gravity works the same, there's no need for a pressurized suit, and even propellers work just as normal! Later games gave Ratchet some sort of commando suit, which kind of made more sense.
Mass Effect 2, when navigating in star system or cluster. All star systems and planets, plus ships and stations are in same plane.
Although the game is careful to point out that this is a feature of the Galaxy Map and not an actual reflection of what the galaxy looks like - its the same reason that the Normandy is shown bigger than whole planets and how you can fly it through suns.
Mothership Zeta from the Fallout 3 DLC of the same name. One part has you take a spacewalk on the outside of the ship.
World 6 (Outer Nebula) of Super Mario Fusion Revival is Science Fiction themed, taking place in outer space, on alien planets, space stations, and spaceships.
In The Adventures of Lomax, the last world is this. It kind of looks like pieces of moon's surface suspended in space. Despite its looks, the world functions just like the previous worlds and there's no difference in gravity and such.