Research shows that warming up before an exercise makes for a safer and more effective exercise session.
Warming up is just that - making the inside of your body more warm. You should warm up until your body starts to sweat- an indication that you're core temperature has raised by 1 degree Celsius. This should take around 10 minutes of gentle cardio (running, cycling, rowing, cross-training, etc).
When I run I walk for 10 minutes first to warm up. When I work out with weights at the gym I go for 10 minutes on a tredmill or bike at a gentle speed.
Many people see stretching as a fundamental part of warming up. It's still a matter of discussion as far as proof of this goes for all different purposes. I don't think stretching before-hand will be help your running, but it may warm up the inside of your muscles for weight training. Stretching certainly isn't bad for you and if you're muscles ache from yesterday, stretching before you exercise will be a good idea.
I'll go into more detail about stretching in another post.