It depends on how bad the pain is, and what sort of pain it is.

When in the process of lifting, it should not be painful, but it should be hard to do if you want to make MUSCLE GAINS.

DOMS will cause you some pain, but are nothing to be concerned about. These will have you feeling perhaps tender around your muscles.

Joint/bone pain is different. This too can be caused by lifting weights, but should only be slightly painful during the days after you workout. If it is painful while doing a certain exercise, stop.

Any stinging, extremely sharp pains may be more than just an overworked muscle, so see a doctor. Look out for any bruising which has occurred after any pain like this while lifting. It could be a MUSCLE TEAR.

Related Questions:

1. How many sets and reps should I be doing to gain muscle? Do I need to train all muscles the same way?
2. John Boiardi's article Muscle Tears: the good, the bad and the ugly
3. What is DOMs and how can they be treated?