I'm an outlier. I've been homebrewing for about 15 years, and I recently upgraded to a kegerator and kegs, rather than bottling. I used to do a full week in the primary, then transfer to the secondary for about a week, then bottle and wait 2-3 weeks. This (at least 15 years ago when I learned) was textbook. I have recently bought a kegerator and started kegging my beers. I've also been going through beer very quickly, and have been brewing for a variety of events, etc. I've needed to turn around beer quickly, at times.
The last several beers I've moved from the primary to the secondary as soon as the airlock stops bubbling rapidly. Usually, this is about ~3-4 days, though sometimes it's as long as 7 days. I NEVER have left a beer in a primary for more than 2 weeks. It's a bad idea. The primary (plastic bucket), is not designed to be fully airtight. The primary relies on air pushing out any potential contamination. You're asking for contamination if you leave it in the bucket for weeks at a time.
I'll then leave in the secondary for ~a week, or whenever it stops doing anything for a couple days. I turned one around this past week that was only in the secondary for 2-3 days. The aeration helps speed up the process, and while you'll be fermenting some residual sugars after the fermentation slows, the beer really isn't doing much other than getting old.
When I started brewing 15 years ago, the advice was to move things along as soon as the airlock was bubbling less than once every thirty seconds. I still go by this. It works. I don't really get the new trend of allowing your beer to sit in the primary (which isn't particularly airtight), or the secondary (more common) for weeks. Why not put it in the bottle or the keg? It can still ferment residuals and is more airtight than in the secondary!
The other thing to keep in mind is that the hop flavor / character will mellow / degrade over time. Heavily hopped beers will get more bitter and less floral. I've done some complex beers - like a chocolate cherry imperial stout - that aged very well; but most beers are better fresher.
If you're bottling, you can ferment those residual sugars in the bottle, and it will, in my experience, produce a very good carbonation in the bottle (sometimes I've felt like the corn sugar produces an unsatisfying fermentation, even when waiting 3+ weeks in the bottle).
If you're kegging, I've been waiting a day or two after I keg before I force carbonate, to give it one last shot at fermenting the residual sugars. Because aeration/mixing it up ssems to speed up the fermentation process, transferring it 2-3 times will accelerate fermentation. If you notice when you transfer, you always get a quick jolt to the fermentation process, and then it slows / ceases.
Either way, my beer is generally awesome. I haven't been unsatisfied with anything I've ever brewed. A couple brews that I've rushed have tasted a little "young", but not necessarily in a bad way, and I'm not convinced it's due to anything I've done, but sometimes extract beers (especially those that use amber or dark syrup), can taste... well, syrupy. But sometimes other beers from other homebrewers taste rather stale or like they're "old".
The moral of the story is that sure, your beer may be a little crisper if you wait a few weeks in the secondary or age it in the bottle, but at least - when I started brewing, the advice was to move to the secondary as soon as you're not worried about exploding a glass carboy - ie - after 3-7 days!), but I don't understand why you need to age your beer in the primary or secondary, as opposed to in the bottles or in the keg. If you're bottling, it's going to be sitting for a couple more weeks regardless. You might as well get it into the bottles sooner (though you REALLY don't want explosions, which I've never experienced, but I've had friends who have).
I only have one new carboy, and would like to wash it out and get a second brew going asap for halloween. 
