I always seem to write about running on sore legs. I guess it is because I always seem have sore legs at the beginning of a training cycle. Over time, you learn some tricks, how to listen to your body, and if actually running is a good or a bad idea. Long story short, the answer to the question, "Should you run on sore legs", is yes. Maybe.
I run on sore legs, but not before making sure the soreness is because of muscle fatigue rather than injury. Thankfully, the injury part is not as common for me, and the soreness is just something that occurs on a regular, seasonal basis so I've gotten pretty good at spotting the signs.
Here are the top 3 areas of muscle soreness from running that I come across on a regular basis when starting a running plan.
1) Hamstring - running to fast too soon 2) Calf Muscle - from running hills too soon 3) Shin (Tibialis anterior) - from running to far to soon
The best remedy I've found to get past the soreness and on to happy running is to always stretch and massage the muscle groups listed above before and after a run. Don't try stretching to hard while your muscles are not warmed up to avoid pulling, tearing, or ripping them. That would suck.
Oh, and do all the other stuff everyone else says to do like: drink plenty of water, increase your weekly mileage slowly, and get some rest (sleep).