This article is from the Fitness FAQ, by Jeff Gleixner (glex@cray.com) with numerous contributions by others.
YES! The muscles should be work from largest to smallest. If you
already have enough size in most of the large muscles then work
your weakest body part first. The muscles should be worked in
this order: quads, chest, back, hamstrings, shoulders, calves,
triceps, biceps, forearms/wrists, abs.
Why? To get the most gains the large muscles have to be worked
hard enough to promote growth. If, for example, you worked your
triceps to failure then tried to bench press, to work the chest,
your triceps would be worn out before your chest worked hard
enough to grow.
Avoid working abs and then doing Squats. The abs are a very
important link in doing squats, they shouldn't be tired before doing
squats. If triceps are worked before the chest make sure to lower
the weight when working the chest.
 
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