Would it be much more work to create a 3D game on a planet rather than on a flat plane? What engines would support this and what techniques would I use?
An example would be a small sphere the player could walk around to get back where they started.
There's a nice article over at Gamasutra that explains the physics in Super Mario Galaxy, which is probably what you're looking for.
Basically they use the inverse surface-normal of the closest polygon underneath the player as gravitational force. If the player moves over to another polygon while in the air, they interpolate the normals to smooth motion and orientation of the player.
I don't think there are engines who specifically support this, but in general it's not all that complicated.
Instead of translating bodies purely linearly, you have to move it according to it's distance from the center of the planet, as well as depending on it's angle between the body-center_of_planet line and your coordinate system's axes.