Again, it's ONLY one player. No multiplayer component from what I can tell. Much like The Sims...
I'm not so sure thats the case after reading the following, it seems there's some kind of multiplayer component.
Spore populates the universe with creatures and cities created by players from all over. There's almost nothing in the world that wasn't at some point created by another player. Wright discovered someone else's civilization, a curious four-legged race who carried tridents and lived in cities with pointed walls and towers. What happened next was entirely up to Wright: he decided to try to communicate with the other species using a bizarre Close Encounters style mini-game. His UFO played music and waited for the aliens to respond.