China and Russia do wish to expand, but they're not going to do it while the US is in power at least.
The closest we've got is "spread democracy to the world", which is less a "conquer the world" spirit, and more of a "make the world like our way of thinking" cultural expansion. We do it through movies, literature, debates, exchange programs and so forth.
And... erm... conquest. But only rarely (Iraq, South Korea). And whenever we do it by conquest, the US Population seems to get really pissed in general. Its why we had such a "hands off" approach in Libya and Syria so far... and why we're trying to get Iraq out of our hair. (Iraq seems to be a "we broke it we bought it" situation at this point)