I imagine that this will be highly controversial but, well, we're here to ask and discuss, right?!
But there's a problem with that — for every one meta-conscious [sic] SO user who closevotes and downvotes a poor question, there are twenty new users who see the same question and "learn" that this is how SO is to work. Each of those twenty new users goes on to themselves write a lame debug-my-codez-plz post and then our review work, not to mention what I can only imagine to be a ballooning database, is twenty times worse. Rinse, lather, and repeat.
Back to the point, then; again I can only speak for the tags I use so perhaps this is not in actuality a site-wide phenomenon, but the only "new" questions I see now are relatively advanced ones posed by higher-rep users. The basic stuff has all been covered, be it in FAQ form (some tags designate a "co-tag" e.g. c++-faq to mark questions that should be used as common points of reference when marking duplicates to frequently asked questions).
Now, it would not be right to suggest that this means SO should be closed off to non-advanced questions, not at all. On the other hand, is there not a pattern of pretty much all of the rubbish being generated by users with low reputation? Users who write answers and gather rep over their first days and weeks on SO tend to be those who like to put a little thought into life, and thus write questions that may actually be useful for someone someday.
Would it really be such a bad thing to have new users wait this kind of amount of time before asking their first question? Why is everyone in such a hurry? If we can promote the use of brainpower as opposed to "my first port of call to solve this problem is posting it on Stack Overflow" then so much the better — along this line of reasoning is the notion that if somebody needs to post their question right damn now then it's probably the case that they haven't applied the necessary patience to properly solve a problem and learn from it too. Do we need to allow new users to post their first question right from the outset? Is that a priority? Making the barrier to "get help" in any form as low as possible? Or does the fact that the answers to the common questions are now all already there override that to a degree?
I think we can put a stop to the constant influx of nonsense questions into the SO database that take up valuable search result space and just generally cause a nuisance for the benefit of just one person, without losing our ability to help people and provide the information that we set out to provide... and without introducing any sort of elitism, since everybody can gain rep — it takes time, not expertise (at least, not beyond the very basics of the topic in question).
This has been raised before, of course, but two years ago, before this perceived "saturation point" was reached.
So, here it is.
How about this: I propose a minimum reputation requirement of 500 to ask questions.