Don't get me wrong: they have an exceptionally long runway so this won't happen anytime soon but I think it will end up being acquired by the likes of Facebook, Google (disclaimer: I work for Google) or Apple.
I don't see a compelling reason for Facebook to buy Twitter other than to deny it to the other two (which could be compelling but given the direction of their stock price this seems like a hard sell to Twitter's investors and board).
Apple could marry its mobile ecosystem, particularly the messaging infrastructure, to Twitter and be a dominant player.
Google could do the same thing but I think Apple has the most to gain from picking up social assets (note: these opinions are strictly personal views).
Given that it makes sense for Apple to buy a stake in Twitter. Large(r) companies often do this. It's a poison pill. Take a large enough stake and you can make it more difficult for others to acquire that company and be int he box seat to be the acquirer if it should come to that.
I believe that if Twitter gives Apple, say a 10% or bigger stake, they are insuring an exit strategy if they can't continue to exist independently.