I've recently asked a question on meta to which I received four very useful and equally "correct" answers. Each added value; each was helpful to me. Although one answer did receive more votes than the others (8 to 6 to 3 to 2), I'm not sure there really is one answer that is more acceptable than the others. Am I under any obligation to accept an answer, or can I just let it stand as is?
There is no obligation to accept answers if you don't want to, no. Especially now that there is no 'accept rate' given to users to show how many times they accept answers. As you point out there isn't always a correct answer, there could be multiple correct answers, or there could be only one rubbish answer.
What you can do if you're feeling generous is award a bounty to each of the answers - you can do that to multiple answers. That's a way of rewarding multiple answers on one question. But that costs reputation so doesn't get used very often.
If you like them all then upvote them all and don't be too concerned about accepting if nothing stands out as 'the' answer.
If the answers are different, but all correct, I would upvote all of the correct answers, and accept the one that I actually use.
If the answers are all the same, but came in at different times, I would accept the one that came in first, unless one answer was more clear or went into greater detail.
Pick the one that is better because it is
contains more source code contains shorter source code explains things in a simpler way explains things in a more expilicit way is written funnier is written more seriously...
...or whatever criteria appeals to you that distinguishes one answer from the other. So far I have seen quite a lot of questions with similar answers, but there were always differences, and I would always have been able to find some tiny thing to help me pick one of them as my preferred answer.
You're never obligated to accept an answer at all, although it's helpful to do so if there's a correct answer. Selecting a correct answer marks the question as answered, and that saves other people time.
Often, in the case of multiple correct answers, people will choose the first correct answer to be posted, or just the one that they like the best or found most clear/helpful.