I've got a Dubbel going on it's 6th week, but I would recommend 21 days for a normal gravity brew, at least 28 days for higher gravities in the primary. My dubbel may even go on a 7th week due to a family birthday this weekend, so we'll see what happens.
Longer primaries have made a definite improvement on the overall flavor in my brews.
Even when the yeast are largely finished with the primary fermentation process, if left to work longer they will clean up a lot of their own by-products, usually resulting in a cleaner flavor. I also noticed that I often get an extra point or two drop in FG since I started leaving them in primary longer (compared to the same recipe done with a shorter primary). In addition, after a 2 week primary - 2 week secondary and 3 weeks bottle conditioning, 90% of my batches have lost their green flavor and are ready to drink.
I prefer to secondary most of my beers, but many folks on here skip the secondary and instead opt for a 3-4 week long primary. I started out using the 1-2-3 method but as my brewing progressed (and my pipeline built up) I increased my primary time to 10 days, then to 14 days and I'd definitely say my beer has improved.
I'm in the same boat as ifishsum. 2 weeks - 2 weeks - 3 weeks for me. And I too have noticed an increase in quality. How you choose to do your process comes down to the equipment you have at your disposal and your patience.
Don't drink so much, and you won't get a hangover. I hate it when people say this or that doesn't give you a hangover, let me tell you, if you drink enough of any alcoholic beverage you'll get a hangover.
I have never used finings - I generally use irish moss in the boil and most of my beers clear very nicely over time. Patience will yield the biggest improvement in your end result. I always go 3-4 weeks in primary and straight to bottle. Three weeks at room temp to carb properly and enjoy.