I play it sometimes with my brother on our own private server.
Really, for me it's all about adventuring through dangerous caverns and building stuff, like virtual LEGOs. But it's much more than that.
I especially like making mine cart systems and "machines" using redstone.
And like internpete said, there are a bunch of mods you can add that nearly change everything. Like the NPC mod, or the one that lets you modify how powerful monsters are (if you want your adventures to be a bit more dangerous).
The possibilities are almost endless, and that's what I think I like about Minecraft the most...it's whatever you want it to be.