I warm up with light stretches and moderate work on the bike, cool down with final five min. of moderate effort on bike, too. I stretch before and after riding -- when I'm smart. +100 to Ken, who said the older you get, the more important it is. Yeah, when I only have an hour, it's annoying to take 15 min. of it for warm up/down, but I don't even think about it anymore. It's just part of the workout.
As to why, the smartaleck response is -- Stop warming up/down, and you'll eventually find out why you should. ;-) More seriously, it's to avoid injury and to be more gentle with the body before we pound it. Hopefully, we'll all be riding for decades to come; this helps make sure you'll be able.
I stretch for a long time before and after rides. I would LOVE to be able to skip this. When I do, I often get injured. It may not hurt you right away, but generally, you'll pay if you don't do your necessaries.