When I weight-train, I switch from upper body to lower body with no rest.

The main reason for resting between sets is to give the muscles time to recover. If you're not lifting to fatigue (i.e., lifting until you can't possibly do another repetition), it doesn't take as long for your muscles to replenish their energy supplies and recover. In that case, switching to another muscle group after a set is a great way to speed up your workout and keep your heart rate elevated. However, if you're totally fatiguing the muscle (say, by doing a low number of repetitions using high weights), you should rest in between sets. After intense lifting, it takes about three minutes for the muscles to recover and replenish their fuel. During this time, blood is rushing to the area, bringing in nutrients. If you're busy working another muscle group in the same way (high weights, low reps), you're putting a double demand on your blood supply and you won't get maximum performance out of either muscle group. The bottom line: If you're working each muscle to total fatigue, rest for two to three minutes between exercises.