There's two basic ways to approach this:
1) Use spherical coordinates for everything, and use great-circle calculations for direction, movement, distance, et al. These are very hard to make fast, since you have to give up all straight-line calculations.
2) Invent a tile-based system that more-or-less evenly tesselates over a sphere. Plan on spending lots of time looking at soccer balls and such, and thinking about 72-degree angles.
Both of these approaches are much more difficult than you might think. We looked at both approaches for our current game and eventually settled on #2. However, in the process we had to invent an entire coordinate system that is then used for distance and direction calculations. In retrospect, we might have done a different type of game if we had known how hard this was going to be.
You will basically not be able to use a lot of existing algorithms for your game, because they are mostly assuming flat surfaces. Plan on spending a *lot* of time on just getting basic geometry stuff working correctly. And don't get me started on sphere-based navigation and camera positioning...
On the other hand, having gone through the pain and ending up with a pretty cool system, I can say that the end result may well be worth it.
Being able to fly (or walk) all over an entire planet is actually pretty cool...
Also, a lot depends on what kind of game you are making. If you just want to do collision detection on a sphere for purposes of placing a 3D model, then it's easy. But it gets harder real fast when you start talking about movement.