I just started playing it a few days ago, and thus far it's awesome. It kinda like Minecraft with more of an emphasis on exploring and combat. There's less to do as far as the creativity aspect goes (the "wire" system is significantly less deep than Minecraft's Redstone, for instance), but there's a lot more motivation other than "get more material to build more stuff." Boses to fight, interesting biomes to explore (Underground Jungle, "Corruption" that's eating away at the landscape, etc), dynamic events (Remember that Blood Moon that was promised in Minecraft but was never implemented? Terraria has it), tons of weapons and items with tons of enemies to try them on (this game has exponentially more content than Minecraft does), and still a fair amount of building possibilities on the side. So it's the perfect game for people like me, who loved Minecraft for its adventuring and saw the building as a side activity.
I checked out multiplayer really briefly, but was turned off of it for the same reason I was turned off of Minecraft's multiplayer... you can't just bounce from server to server, since most of them impose building restrictions.
I still think Minecraft is an awesome game, but Terraria is a little more to my liking.