I found myself wondering pretty much the same thing about 2 weeks ago. Everyone's motivation is going to be a little different, but here goes:
Some SE sites attract a more transient crowd as portals to ask for quality suggestions (Workplace for ex.), while others allow users to discuss issues which they are passionate about in a constructive way. It's nice to have like minded people to share your ideas with, and to get their feedback.
2. Well Managed
Unlike most other sites SE is very well policed, and the content is kept on-topic. It's nice to see that trolls or idiots are dealt with, and not allowed to run amok. The community events (such as Hats) are also pretty nifty.
Mostly due to the above I find that SE offers very high quality answers, unlike the 1 word replies you'll get on some forums. People actually take the time to answer your question in detail, and the traffic is high enough that you rarely have to wait too long for one.
Because the SE sites are better structured not just anyone joins. A troll, or someone who doesn't put any effort in their posts is going to get discouraged and leave. That means that the users who are actually interested in replying will get their message across, and not simply drown in childish BS, and spam. It's satisfying to know that your answer is reaching people.
5. Reputation and Badges
SE has a good participation and quality reward system implemented. It's thrilling to watch that reputation count go up, and the notifications that you've earned another star are simply the best. It's a good system to reward people who get involved, and to encourage more of the same.
SE demonstrates a lot of trust in its users by allowing us to vote on closing/opening questions, giving us access to some site statistics, allowing - and indeed encouraging - the editing of tags and posts, etc. It's a good feeling to know that your opinion counts, and that your actions are shaping the community. It makes you feel you've got a stake in it.
I hope I've helped you answer that nagging question!