I try to stretch for at least 5-10 minutes before every round, and will usually take upwards of 30 minutes before a tournament. I focus mostly on my hamstrings, inner thighs, shoulders, lower back, forearms, and hands. For most I would think the shoulders and back would be most beneficial. For my shoulders I prefer to stand in a doorway with my arms extended out to my side, leaning into the doorway so that my arms are pushed towards my back a little. For my lower back I lay on the ground flat on my back, and pull each knee into my chest and hold it for a while. After that I stick each leg into the air and slowly move it closer and closer to the ground on the opposite side (right leg moves toward my left side), bending slightly at the knee and holding it with the opposite hand. Then I'll usually stand up and do some trunk twists until I feel loose.
There have been many times where I got a little over-zealous with my stretching to the point that I wore myself out before I even picked up a disc. I try to stretch slowly and only a little bit at a time now...
...and don't forget to get well hydrated before the round, or even before you get to the course if possible.
Edit: one of the reasons I take so long to stretch before tourney rounds is that my stretching time doubles as my meditation / get-mentally-focused / clear-my-head time, which to me is most important before a tourney round.