Leroux: Well, I do have friends but at least regarding videogames I'm not much of a teamplayer; I actually enjoy some games more on my own than in the company of people pressing me on instead of letting me take my time and look at the scenery. ;)
Is there a story of sorts, an ending to reach, like in a metroidvania game, or is just about getting more and more powerful for its own sake, like an MMO?
It does have a story, but it's loose... there are "recruitable" NPCs (they'll appear and stay in housing built for them) which give you hints and directions on what to do. And, basically there is an "endboss", but if you know where to go you can head straight for it - though without decent tactics and equipment I don't think he can be beat - which after he's defeated the game enters 'hardmode', with new biomes, material and tougher enemies appear, elements of "good and evil" start spreading... but again, whether to deal with or ignore the new environment is mostly your own choice (except for the fact that almost everywhere becomes more dangerous to explore, heh).
Smannesman: Since the dev went on to make Starbound, it's a lot like that in case you've perhaps seen/read more about that game.
The dev did NOT go on to make Starbound (which without modding still feels very shallow to me compared to Terraria, though admittedly it's still early in development), but Starbound's head dev was the pixel artist on Terraria for a time, before starting his own team. Terraria's dev is starting work on Terraria 2 sometime this year.
There are a lot of "Terraria-likes" in some stage of development; the best one I've played so far is Darkout, which while it is very recognizably unfinished, already has a stronger implemented story than e.g. Terraria and Starbound.