I won't rehash the style and form issues already so well covered but want to emphasize a few of points of personal interest.
Curing Genuine Ignorance - I enjoy alleviating genuine ignorance, a.k.a., teaching serious students. Even if it's merely polishing another's semi-ignorance into fuller understanding, I enjoy formulating answers.
Improving Personal Understanding - There's an old saw about the best way to learn: "see one, do one, teach one." Teaching usually improves one's own grasp of a topic. The need to cast an explanation into terms another finds comprehensible can require the attainment of deeper personal understanding. This is especially true when the first answer fails to educate the questioner...having to develop an alternative answer almost always demands rethinking that gains new perspective for the answerer.
Expanding Public Awareness - Some questions serve less to gain the asker a much enhanced grasp of the topic as to place the topic firmly into the public view. Even if the asker is not ignorant, raising public awareness and inviting alternative explanations is valuable. Robust discussions that arise in the context of competing and/or complementing answers can generate new insights for all, regardless of pre-existing expertise.
So, for me, good questions provide opportunities to cure genuine ignorance, improve (my own or others') personal understanding, or expand public awareness of a topic.