I sometimes give hints, and sometimes full solutions.
The reason is that sometimes I am unsure of my ability to write a complete solution, but I know what is the correct way of approaching the problem (and I usually prefer wasting my time doing something else, and not filling the details myself).
Other times, however, I feel that I can give a very good account of all the details. I think this can be very helpful and instructive. Not all people who come here to ask help in their homework are looking for final solutions, some want to learn but their local environment is not well-suited or they might have teachers which are poor educators and it's hard to follow them.
I prefer to think that people who write properly formulated questions really want to learn, but could not do it outside this site. Of course that when someone merely spits a question from the questions sheet (or worse, e.g. "hurry up guys!") I will avoid giving any help at all.
However, when I want to help someone, I want them to fully understand what I meant. Hints can be hit-miss sometimes, but giving a complete solution to a problem means that you have the opportunity to explain the relationship between the propositions and the reasoning you apply. I like doing that.
Even when students come to me in office hours just to ask how to solve one specific question, I often end up giving them a bunch of theory too. During the fall semester when I taught math/comp. sci. students they liked it; now when I teach engineering students they like it less.
Of course when there are users which I see constantly asking questions from homework, I may prefer to switch to hints again because I fear they might not be trying hard enough to chew on their own.
Now comes a good point to think about it. If we want people to learn mathematics, and we really just want them to learn it. I was told (and I agreed since then) by one of my teachers that the only reason they require us to submit homework is that they want us to work on the problems, if they knew we would do that there would have been no submission of homework. However other courses already ask us to submit homework so we would do those first and not give any time to that specific course. Therefore all homework is for submission.
So we want people to chew on the problems chosen for the homework sheets, because those are often the problems which require the student to exercise the definitions and the theorems and are usually chosen for a specific level of education. But the problem, again, with posting full answers is that we want them to chew on the problems on their own, I agree that this is the only way to advance in your studies.
Alas, if someone is reading on their own. The book is well fitting to their level, but they come with questions from the book, and they come and ask and ask and ask. It would seem that they are not trying to solve the problems hard, if they don't see a solution right away - they come to ask for help. This is bad because when you struggle with the problem you learn a lot more.
Now ask yourself, would you have answered in full the questions of someone who was self-studying a certain topic? Is this any different than a homework sheet? Yes. It is different because of honor code.
But my goal is to educate not to be a moral compass, if someone wants to learn - I will do my best to help them learn.