I just went through the Best Buy process, and couldn't be happier. After a co-worker did a number to my Evo, I took it into the Geek Squad. The bad news was that, contrary to what any salesman may have said, you do NOT get a new phone on the spot. It goes to the repair center. All told, I was given a new Evo less than two weeks after I turned my broken one in when the repair center determined it wasn't cost-effective to fix my broken one.
I think it depends on how badly damaged your phone is. If the screen (down to the digitizer) is cracked, you're getting a new one and it shouldn't take too long. If it's some other damage that isn't too severe and can be repaired, it will probably take longer. Having read some of the "over a month" horror stories, I was anxious that I would be in for such a long wait, but I wasn't. Nice thing was, you get to keep your micro SD card and charger; that's worth $20-$40 depending on where you could buy them? When they give you a new phone, you get the whole kit.
The worst thing about the whole process is Best Buy's crappy update system...pretty worthless and not timely, so you're always guessing what's being done to your phone.