Keyframe mentions a good approach, but I'll offer two more:
1) Design your game for multiple resolutions/aspect ratios. The idea is to take advantage of every bit of the screen real estate, but "design out" any advantages that one aspect ratio might have over another. Depending a lot on the game, different aspect ratios may still have an advantage over others, so you'll want to keep that in mind for things like multiplayer matchmaking, leaderboards, achievements, etc. if any of these are relevant.
2) Use the extra space for more HUD / chroming. Pretty much what Keyframe said as far as having a baseline or minimum resolution supported, but instead use the extra space for something other than the game action.
The big disadvantage with the second approach is that if you take something very square-ish as your "safe zone," you leave a lot of unused / unintentionally used pixels in a widescreen setup.