There is overwhelming evidence that doing a warm-up before performing an exercise both increases your performance and reduces your risk of injury. I know of no one in their right mind that does not doing a warm-up before performing strenuous exercise. And I mean literally nobody.
You can read about the benefits of a warm-up in more detail here: http://exrx.net/ExInfo/WarmUp.html
My take on it is this: stretching promotes flexibility, and flexibility is beneficial. In my personal experience, stretching before prolonged aerobic activities like running will make you feel less awful while you do those activities. Some studies suggest you can run fractionally faster if you don’t stretch first, but most people are concerned with not being in pain while they run, not fractional speed gains.
Conversely, in my experience stretching does little good when lifting weights, and I only do it if my muscles are feeling unusually tight before the workout. This is just to feel more comfortable while working out, not for a specific performance benefit. Note that I do a good specific warm-up (see above) before I lift.
Also, if you get a cramp you will want to gently stretch the cramped muscle. So you will want to know how to stretch the big muscle groups for that reason, if nothing else.
I have linked to a list of major stretches you will probably want to learn.
Lower body:
Quadriceps stretch:
http://exrx.net/Stretches/Quadriceps/Standing.html
Calf stretch:
http://exrx.net/Stretches/Gastrocnemius/Lunging.html
Hamstring stretch:
http://exrx.net/Stretches/Hamstrings/Standing.html
Groin stretch:
http://exrx.net/Stretches/HipAdductors/SeatedGroinFloor.html
Glute stretch:
http://exrx.net/Stretches/GluteusMaximus/Lying.html
Torso:
Abdominal stretch:
http://exrx.net/Stretches/RectusAbdominis/Prone.html
Lower back stretch:
http://exrx.net/Stretches/ErectorSpinae/Cat.html
Upper body:
Chest stretch:
http://exrx.net/Stretches/ChestGeneral/Doorway.html
Lat stretch:
http://exrx.net/Stretches/LatissimusDorsi/Overhead.html
Tricep stretch:
http://exrx.net/Stretches/Triceps/Overhead.html
Bicep stretch: