Just under a decade later, we won the race to the moon. Now we are nearing the end of US manned flight (in government spacecraft at least) with the end of the shuttle in a couple months...after a few more delays I'm sure. What's next? Soyuz tickets will be bought for great amounts by NASA to send our people up there to the ISS, maybe they can get some kind of season pass for a few years?
My bets are on SpaceX and the Falcon 9/Dragon spacecraft that will be the next manned orbital vehicles from this country. The next manned spacecraft will most likely be the $200,000/ticket Virgin Galactic Spaceship Two flights to space (similar to Shepard's flight, just enough to get your toes into space and back again).
Space Adventures is planning tourist flights to the moon on modified Soyuz spacecraft. The plan is for rich folks to make a stop at the ISS, then board another spacecraft for a ride around the far side of the moon and back. Maybe private companies will be the first back to the moon (at least around it in Apollo 8 style)? But who will be the next to step on the surface? Probably Chinese!