Here is an excellent excerpt regarding rest from the Encyclopedia of Modern Bodybuilding written by the famous Arnold Schwarzenegger:
It is important to pace yourself properly through a workout. If you
try to train too fast, you risk cardiovascular failure before you have
worked the muscles enough. Also, you may have tendency to get sloppy
and start throwing the weights around instead of executing each
However, training too slowly is also bad. If you take 5 minutes
between each set, your heart rate slows down, you lose your pump, the
muscles get cold, and your level of intensity drops down to nothing.
Try to keep your rest periods between sets down to a minute or less.
In the first minute after a weight-training exercise you recover 72
percent of your strength, and by 3 minutes you have recovered all you
are going to recover without extended rest. But remember that the
point of this training is to stimulate and fatigue the maximum amount
of muscle fiber possible, and this happens only when the body is
forced to recruit additional muscle fiber to replace what is already
fatigued. So you don't want to allow your muscles to recover too much
between sets - just enough to be able to continue your workout and to
keep forcing the body to recruit more and more muscle tissue.
There is one other factor to consider: Physiologists have long noted
the link between maximal muscle strength and muscular endurance. The
stronger you are, the more times you can lift a submaximal amount of
weight.; This means that the more you push yourself to develop
muscular (as opposed to cardiovascular) endurance, the stronger you
become. So maintaining a regular pace in your training actually leads
to an increase in overall strength.
The sweet spot for promoting size, endurance, and strength is 1 minute. Taking only a few seconds of rest would only promote endurance.
Longer Rest Periods for Strength
In another part of the book, Arnold talks about the occasional days which you should train heavy. By heavy, we mean going to failure in 6 reps or less. Arnold believed that bodybuilders should occasionally train heavy like power-lifters to get a hard dense look. In these days, he suggests longer rest periods, perhaps up to 3 minutes. This longer rest period would prevent cardiovascular failure from short-circuiting muscular failure.
Powerlifters, or people training for strength (as opposed to bodybuilders, who train for muscle size), may have occasional need for longer rest periods between heavy sets. Five or ten minutes between sets is not unreasonable for very heavy sets of squats, or chin-ups to failure, for instance.
Research and weight room experience shows that longer rest periods produce more strength and power, whereas shorter rest periods produce more hypertrophy and muscle mass:
When training for muscular strength, the magnitude of the load lifted is a key determinant of the rest interval prescribed between sets. For loads less than 90% of 1 repetition maximum, 3-5 minutes rest between sets allows for greater strength increases through the maintenance of training intensity.
When training for muscular power, a minimum of 3 minutes rest should be prescribed between sets of repeated maximal effort movements (e.g., plyometric jumps). When training for muscular hypertrophy, consecutive sets should be performed prior to when full recovery has taken place. Shorter rest intervals of 30-60 seconds between sets have been associated with higher acute increases in growth hormone, which may contribute to the hypertrophic effect. When training for muscular endurance, an ideal strategy might be to perform resistance exercises in a circuit, with shorter rest intervals (e.g., 30 seconds) between exercises that involve dissimilar muscle groups, and longer rest intervals (e.g., 3 minutes) between exercises that involve similar muscle groups.