In the past few years, online question-and-answer forums (or Q&A forums) have gone from being an afterthought offered by the occasional project to an increasingly expected and normal component of user-facing services. A high-quality Q&A forum is like a FAQ with nearly real-time updates — indeed, if your Q&A forum is sufficiently healthy, it often makes sense to either use it directly as your project's FAQ, or have the FAQ consist mostly of pointers to the forum's most popular items.
A project can certainly host its own forums, and many do, using free software such as https://askbot.com/ , http://osqa.net/, http://shapado.com/, or http://www.coordino.com/. However, there are also some third-party services that aggregate questions and answers, the best-known of which, https://stackoverflow.com/, frequently has its answers coming up first in generic search engine results for popular questions.
While Stack Overflow hosts Q&A about many things, not just about open source projects, it seems to have found the right combination of cultural guidelines and upvoting/downvoting features to enable its contributors to quickly narrow in on good answers for questions about open source software in particular. (The questions and answers on Stack Overflow are freely licensed, although the code that runs the site itself is not open source.) On the other hand, projects that host their own Q&A forums are lately doing pretty well in search engine results too. It may be that the current dominance of Stack Overflow, as of this writing in 2014, is partly just an accident of timing, and that the real lesson is that Q&A-style forums are an important addition to the free software project communications toolbox — one that scales better with user base than many other tools do.
There is no definite answer to the question of whether or when you should set up dedicated Q&A forums for your project. It depends on available resources, on the type of project, the demographics of the user community, etc. But do keep an eye out for Stack Overflow results, or other third-party results, coming up in generic question-style searches about your project. Their presence may indicate that it's time to consider setting up a dedicated Q&A forum. Whether you do or not, the project can still learn a lot from looking at what people are asking on Stack Overflow, and at the responses.