Apple has confirmed that if you have an iPhone 3G, even though you can run iOS 4.1, you won’t be able to get in on the Game Center loving. On their official page on the matter, they point out the service is compatible with 2nd, 3rd and 4th gen iPod Touches, and iPhone 3GS/iPhone 4. iPhone 3G users are out of luck.
Man, more and more the iPhone 3G is being treated like the redheaded stepchild of the iOS family.
That said, I’m willing to bet that there’s a technical reason behind this. Since the iPhone 3G can’t handle multitasking, it might not be able to handle the background processing required for Game Center to be able to keep up leader boards, invitations, achievements and the like.