Actually muscle soreness can be an indicator of a good, successful workout, but it's important to understand the difference between the two types of soreness that can occur.
Lactic Acid Accumulation.
Soreness immediately after exercise is typically due to Lactic Acid Accumulation. Lactic Acid (or lactate) is a byproduct of exercise which occurs when there is too much pyruvate (produced through glycolysis) and not enough oxygen present to use it for ATP production... when this happens, the pyruvate becomes lactic acid (which can actually be reabsorbed and used but that's a whole nother story).
Delayed Onset Muscle Soreness.
Or DOMS is soreness which occurs 1-2 days post exercise and is caused by the microtears in your muscles which form during intense exercise. This damage causes an increase in nucleation of the muscle fibers which leads to increased muscle growth.
From my personal experience and education, I believe that DOMS is a good indicator of exercise, but it's important to allow your body plenty of time to recuperate during this period of muscle reconstruction. If you're doing a full-body workout, chances are your whole body will be experiencing DOMS and you should let your WHOLE body rest. If you're doing a split routine (upper/lower body), then you should be fine working one part when the other is still recuperating.
Eventually, after having trained under a routine for a while, chances are your body will adapt and you'll no longer experience DOMS. At this point I recommend modifying your routine, by either mixing up your routine order, trying new exercises, or perhaps building a whole new split (4 days vs 3 days, upper/lower vs push/pull, etc). I fully believe in the "shocking your muscles" phylosiphy, as even something as simple as doing pull-ups before dips (instead of vica versa) is enough to cause extra soreness after a workout.
Anyway, that's my oppinion. In the end it's really about what works best for you.
