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.
The best form of warm-up is to do a less intense version of the specific exercise you are about to do. This both warms you up generally, and prepares your muscles and joints for the specific range of motion and type of load that you are going to place on them. For weights, before you do each lift do 10-15 reps at 50% of your working weight for the lift, then rest a minute or two before starting your working sets. For cardio, do a few minutes of the exercise at reduced speed and then rest a minute before going all-out.
You can read about the benefits of a warm-up in more detail here: http://exrx.net/ExInfo/WarmUp.html
Stretching is an interesting topic. The overwhelming conventional wisdom is that stretching is beneficial. But there are people who will go mental if you bring stretching up, because of the lack of hard scientific evidence that it actually works to prevent injury or improve performance. Some advocate dynamic stretching for its supposed performance benefits, while others suggest avoiding it due to the increased risk of injury. And so on.
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 back stretch: