Stretching

Flexibility is very important for everyday activities like walking, cleaning, and gardening. If you lack flexibility you will have to compensate by contorting your body and will end up injuring yourself. Flexibility is also very critical for almost every sport. The further a swimmer can reach their hand before plunging it in the water, the faster they will swim. Gymnastics is a perfect example of a sport that requires incredible flexibility, imagine someone without flexibility trying to do the beam or a floor routine - not possible. 
Now lets talk about flexibility in bodybuilding. First, lets get rid of the muscle bound bodybuilder myth who is so muscular they cant scratch their back. Bodybuilding does not make one inflexible, not stretching makes one inflexible. If a bodybuilder (or anyone else for that matter) does not stretch, they can lose range of motion.
"Common wisdom" is that you must stretch before working out with weights, I disagree with this. From what I have seen, the danger of injury from pre-workout stretching is much greater than the lifting weights itself. In my opinion, the best way to keep from getting injured while lifting weights is to do warm up sets at 30%, 40%, 50% and 60% of their usual weights before getting started. I would normally do this 5min warm up before my first exercise for each muscle.

 There is one theory I have read that claims that the way to get the muscles to grow is to stretch them while they are pumped which is between sets, I am skeptical. As you know, I personally don't like the idea of stretching between sets, I think it disrupts focus too much.

Stretching can be far more hazardous than bodybuilding and muscle pulls can take a very long time to heal so you need to make sure you know what you are doing. I would strongly recommend getting instruction by taking a yoga class, you need to learn how much you can force the stretch safely without injuring yourself. Of critical importance is that you stretch slowly without bouncing or jerking. Those bouncing toe touches that us oldsters were taught in PE class are BAD, no bouncing!

If you only have time to do one stretch then do hamstrings because that is typically the tightest muscle in the body and it can lead to back pain if it is not flexible enough. Since I have a history of lower back pain problems, the hamstring is the one that I am the most religious about.