Are we doomed to a future in which we are mere vassals to a burgeoning and aggressive Chinese hegemony? If you vote for Barack Obama, yes! In fact, according to Mitt Romney, he's actively working toward such a future.
But seriously. Are we? I don't think so. Sure, China is going to grow and there will inevitably be some shifts in influence as that happens, but if I had to make a 50-year bet on any region of the world, I'd pick the United States. Europe has demographic and growth problems; Russia is doomed once their energy resources run out; Africa will remain a basket case for the foreseeable future; India is starting from a poor base and I'm not convinced they have the governance or institutions to maintain rapid growth over the long term; and China — well, China has its problems, as I've noted multiple times in this space.1 I don't think they're going to collapse or anything like that, but I do think their growth will inevitably slow down long before their per-capita income is anywhere close to ours. It will likely take them at least a century to catch up.
Meanwhile, the United States is really in pretty good shape if we can just get our political affairs in orders.2 Compared to the rest of the world, our economy is pretty solid, our demographics look good, and we have more energy resources than most other rich countries. Dan Drezner has more here. It's worth a read if you want to see the optimistic case for American influence and wealth in the 21st century.
1And what about South America? I'm not sure. That's why I didn't include them in my list.
2Yes, yes, I know.