So Pokemon GO isn't out yet, and therefore I can't really include it on a list. But what is out is Pokemon GO's spiritual predecessor, Ingress. This game offers an incredibly unique multiplayer experience in the physical world, requiring travel and exploration for success.
In general, the game is about joining factions and exploring real world environments to claim landmarks for your team, gather items, and gain experience. What makes Ingress so great is that its community is so huge and welcoming. In most cities worldwide, there are groups to join that play the game together and coordinate their actions to help their team operate more successfully. It really is a completely different multiplayer experience, and it's worth checking out, especially if you need some fresh air.