I NEVER lift a weight without hoppin on the elliptical or bike for 10-15 min and then stretching. If you don't want to stretch the muscles you will be working you need to stretch 2 very important areas. The back and core are involved in almost every exercise whether you realize it or not. Any of you that have had back problems or an abdominal strain/hernia know exactly what I'm talking about. You think that when you are pushing big weight on the flat bench that your pecs, delts, and tris are the only thing taking a beating? Guess again.
For awhile now I've been an advocate of stretching my whole body pre and post workout. Although preworkout stretches after a warmup are very important, I still think post workout stretches are the most neglected. In fact, I like to "mirror" my workout if you will. I'll do 10-15 on the elliptical, stretch for 5-10, then hit the weights. When I'm done I'll stretch down and then hit the elliptical or the bike again to help maximize bloodflow post workout. Keep in mind that these are short times, if I was hitting the bike or elliptical for an hour after hitting the weights I would imagine this to be catabolic and counter-productive. The method I use has worked very well for me, but everyone is different. Everyone has their proven method, but as we age we need to focus a lot more on injury prevention and allowing the muscles adequate recovery time.