Is it impossible to accept a question I asked 2 months ago or something?
I cannot hit the "accept" button on an answer, as illustrated below.
The existing accepted answer to this question used to be true (I even upvoted it, on May 12, at 14:53), but no longer is.
As of June 2010, the bounty system has nothing to do with accepting answers. Now, you are allowed to accept an answer to any of your questions at any time*. You are also allowed to remove "accepted" status from an answer at any time, and may choose a new accepted answer at — you guessed it — any time.
The bounty time limit has not changed. Even though bounties have nothing to do with accepting answers any more, they still last for exactly seven days and disappear or are auto-awarded if you don't award them manually at the end of the seven-day period. Convenience link to bounty FAQ
*: there are still a few edge cases where this isn't strictly true; you can't accept an answer within 15 minutes of asking the question, or a self-answer within 48 hours. But, again, those are edge cases.
Edit: This answer is no longer correct. See Popular Demand's answer instead.
It is always possible to accept an answer, except in bounty questions. Bounty questions should be accepted within a week, if that does not happen (only possible if there are no or no upvoted answers) then no answer can ever be accepted.