Answering for myself (>100k rep on SO, >3000 answers, 61 questions):
There are areas where I hardly ever need to ask questions, but mostly I find solutions to my problems by looking at the code (often in a debugger) asking colleagues, reading documentation and searching for error messages or a combination of carefully chosen keywords on Google (and quite often that leads me to existing and answered questions on SO).
I'm sure that in some cases I would have gotten a solution more quickly by asking on SO, but I prefer searching actively to waiting passively.
And @Daniel B's comment is also on to something: The questions I can't quickly find an answer for on the web tend to be difficult, which means they take longer to get an answer and may even get none.
Dirty little secret: quite a few of my answers are actually the result of seeing the question and thinking "I'm sure I can easily find an answer for that on the web!" despite knowing very little about the subject matter.