Sure, some games have a widescreen mode. Soul Caliber 2, Madden NFL, some others... However, most games do not. I would expect that more games will include this feature as time progesses.
I think it's pretty much the same situation with PS2 and Xbox.
If you have a widescreen TV, you can still put your TV in widescreen mode and play the games that way, even if the game doesn't have a widescreen mode. The aspect ratio is wrong, but it looks fine for games. That's what I do.
-Ryan