- I voted to close this question, since it was unclear/low quality. If the user edits the question, I want to see that there were changes, so that I can vote to reopen if it was sufficiently improved.
- I downvoted the question - if the OP edits the question, I might remove my downvote. I favorited it so that I notice any changes.
- The question is poor, but one the answers contains information which is interesting to me. I want to keep the link somewhere, so I add it to my favorites.
- The question is likely to be deleted, which makes finding it again difficult. Since I want to keep the link because of rather interesting exchange in comments, I favorite the question.1
- This question is rather easy, but it suggests a generalization which seems rather intriguing to me. At the moment I do not have too much time to think about this - I will favorite the question, so that when I check my favorites, I am reminded about this.
- This question is so poor that it definitely should be downvoted. I have already used all my 40 votes today, so I'll mark it and get back to it tomorrow.
- I think that this post is worth editing. But since it is advised not to bump too many posts at the same time, I decide to do that later. So I want to mark the post somewhere. Favoriting the question is a possible a way to do this.
If you look at answers to the questions Why favorite but not upvote? and Would you ever favourite a question you down vote? on meta.math.SE, you will find some suggestions along similar lines. Various categories mentioned in this feature request on main meta can also give insight on how various users use favorites: Favorites improvements - search, categorize, personal tags, add note, favorite answer.