I haven't played many games that are solely about exploration, but some of my favourite games have exploration as a driving force.
There's Love, which I'm sure many people here are familiar with from RPS coverage. A small scale MMO set in a procedurally generated world that is constantly rebuilding itself, inhabited by potentially hostile AI tribes.
Lesser known is Shores of Hazeron, an incredibly ambitious space MMO that's like Spore grown up (and regressed 15 years graphically). You design your species, build up Sim City-style and produce higher tech goods until you're ready for your first space launch. Jetting off from your planet (and probably crashing a few times) in a chemical rocket, you can set up a moon colony to mine materials for proper spacecraft construction. You then design your own ship (tile by tile, very flexible) and begin exploring your solar system and the gigantic galaxy. You can chart the wormhole network, which can take you to distant space quickly, or you could construct a giant colony ship and manually set a course for other stars in the sky.
There's a hell of a lot more to it than exploration, but it all hangs together on the exploration. You want to find more resources to build bigger and better ships. You want to find other civilisations to invade or trade with. Maybe you want to settle as many planets as you can, or find one of the elusive ringworlds: http://www.youtube.com/watch?v=fn7BRf7XSsU.