If you feel strongly about this subject, you probably want to follow this proposal on Meta Stack Overflow: Should we require minimum reputation to continue asking questions?
In a nutshell: After your first 10 questions, it will require 100 more reputation to ask every additional 10 questions. This would also be applied retroactively, so users can be disassociated from their older questions if they didn't get many upvotes. You would need to get 2 upvotes or more on average per question to keep on going without getting rep in other ways.
Update:
We are reevaluating this based on community feedback. The new heuristic to prevent questions being asked will probably be based on a combination of question closes, question deletes, question flags, and lack of significant upvoting, even at very low levels (0.20 etc) -- scoped to new-ish users.
One new change is that you can only ask 50 questions per 30 days. This was initially 70 questions but quickly lowered to 50, and will probably be tweaked in the future.