This is a debate that has been going on in the fitness and athletic community for the longest time, whether to perform full body workouts, body part splits (a la bodybuilding), upper/lower, or push/pull splits.
Today, lets tackle the body part split and the full body workout.
Body part splits work fairly well for several members of the training population. Specifically, they're pretty effective for advanced bodybuilders and people undergoing rehabilitative training. (These are also two groups for whom I think machines are most effective. Pretty much everybody else would be better served by a mostly free weight training regimen.)
Most athletes and gymgoers would be better served by doing a full body split. And, instead of training specific muscles, focus more on training movement. This will result in a multitude of benefits including a greater increase in post-workout metabolic rate, greater calorie consumption during the actual workout, superior neuromascular activation, improved athletic performance, increased strength, more core activation and increased endurance.
This of course doesn't mean that you're doing the same workout 3 days a week, but you're going to be hitting your muscles 3 days a week. You can try the following workout of multijointed, multiplanar compound movements. (These workout are not done superset or circuit style.)
You can precede each workout with the following warm-up:
5 mintues of cardio
20 bodyweight squats
20 pushups
stability ball plan with 30 reps of knee tucks
Workout 1
Deadlifts
Squat with bar push
Chin-ups or pulldowns
Lunge with one arm cable push
Standing two-hand cable rows
Dips
Seated trunk twists with medicine ball
Stability ball crunches
Workout 2
Walking lunges
Dumbbell/kettlebell swings
Dumbbell clean and jerk (one or two hands)
One arm dumbbell deadlifts
Dumbbell bench press (or incline press)
Bent over barbell rows
Decline knee raises
Woodchops
Workout 3
Barbell squats
One arm dumbbell/kettlebell snatches
Bodyrows
One arm stability ball flyes
Standing military press (shoulder press)
Stiff leg deadlifts
Vacuums
Reverse woodchops
Stability ball crunches (or alternatively, flexed-hamstring floor crunches)
I didn't specify load or reps/sets because you should do this workout at an intensity and load that is appropriate for you. Make sure, however, that you are being challenged to see best results.
Good training!