Depends on your current fitness level, age, body type, metabolism, goals, etc. Some signs you may be over-training:
1. you are getting consistently weaker (everybody has a bad day or 2 every now and then)
2. are you always tired, lethargic or feeling depressed?
3. is your body fat increasing, even though you are exercising regularly and eating healthy?
Generally you want to do enough exercise to stimulate muscle growth and no more. Remember, exercise damages muscle and then you need to recover to allow the muscle to be rebuilt. If you exercise too much, do not rest enough or do not get the correct nutrition, you will not get the maximum benefit from exercise.
A good rule of thumb, if you are a beginner, is to perform 1 compound exercise per body part, for 24-30 total reps (2 sets of 12-15 reps, 3 sets of 8-10 reps, 5 sets of 5-6 reps). If you are intermediate you can add a second compound exercise, or 2 sets of 8-12 reps of 1 or 2 isolation exercises.