It is allowed, but that doesn't mean you should.
Some users, like myself, have issues with questions that are not asked in good faith. There are some questions here that were quite clearly asked because a user found a bit of trivia and decided to turn it into rep. That's not explicitly forbidden, but it also isn't very cool.
I would recommend the following guidelines:
So, yes, you can do it, but please make sure it is a worthwhile post. The goal of this site is to provide well researched answers to relevant questions, and the goal of the users should be to make the site as useful and high-quality as possible. You gain rep along the way, but that should always be a side effect, not the end game.
A ton of picture identification questions aren't going to help many people, although they are often interesting and sometimes a LOT of fun to answer, especially when a group of people get together and assemble an enormous CW answer.
Most of the time, you should ask questions because you don't know the answer, but want to learn about it. Questions your already know the answer to should never be more than an occasional indulgence.
And more important than anything else, make sure that the question is worth having here. It should be interesting to other people, at least somewhat significant, useful, worthy of upvotes, and ideally, something that other people might have been wondering about as well.
Questions that fail to meet these criteria should be avoided whenever possible.
Although it goes without saying that we usually don't know whether the OP already possesses the information he or she is seeking unless he or she posts an answer shortly after posting the question, and it is rarely easy to determine with any certainty whether a question was asked in good faith. This means that it is incumbent upon each of us to maintain our own integrity for the good of the community.
Full disclosure: As far as I can recall, I have asked questions to which I knew the answer only twice: once here, once on M&TV. They were both Story ID questions about a particular movie. I asked here first, to see how long it would take for someone to find the (extremely obscure, almost completely unknown and forgotten) movie in question. Months later, I asked it on M&TV to see if they would be faster than SF&F.