I don't check my watch -- I can pretty much approximate my rest times between sets quite accurately.
However, I feel it's critical to bring my log book with me into the gym to record everything. Not just sets and reps, but rep style (strict form, decent form, explosive, partial reps, forced reps, drop sets, etc.), order of exercises (e.g. one workout start off with Incline DB presses, next workout it might be my 3rd exercise and therefore my poundages will be less, etc.), time of the day I'm working out, whether I ate good that day or if I didn't get enough meals in, whether I got enough sleep the night before, approx. length of rest periods between sets, whether I was dealing with an injury at the time.....endless number of factors, but important to record and look back on it and learn from mistakes. I don't know about you guys, but I can't remember all of the things I mentioned above and still work a full time job and take care of my family.