Pullups and dips are complimentary upper-body strength-training exercises. They work opposing body parts, which means that if you do them in the same workout, pull-ups and dips hit all the major muscles of your upper body. How often you do these two exercises depends on your program design and intensity.
Pullups and dips are multi-joint, compound exercises that target several upper-body muscle groups. Pullups mainly work your latissimus dorsi, the largest muscle of your back. However, several muscles in your upper back and arms assist, including your traps, rhomboids and biceps. Dips target your shoulders, triceps and chest muscles. If you perform a dip vertical to the floor, you target your triceps more than your chest. If you lean forward slightly, you hit your chest muscles more than your triceps.
Recovery is an important, but often neglected, factor of a successful strength-training program. The positive adaptations -- strength, power and hypertrophy -- occur when you are resting, not when you are working out. If you do not give your muscles enough recovery time, they cannot improve and may atrophy, or weaken. The National Strength and Conditioning Association recommends that beginners rest at least 48 hours between full body workouts. Advanced lifters, who work out at a higher intensity, should rest 72 hours between workouts that target the same muscle group, but they can work out other muscle groups in the interim.
If you do pullups and dips in the same workout, you should not do them on consecutive days. You would be working the same muscle group two days in a row and not providing your muscles the necessary recovery time. Depending on the intensity of your workout, wait 48 to 72 hours before doing your pullup and dip workout again. The more intense your workout is, the more time your body requires to fully recover.
If you do pullups and dips on separate days, you could do them almost daily. You would be working your chest, triceps and shoulders on one day then working your back and biceps the next day. Your pullup muscles rest on the days you do dips and vice versa. However, the body as a unit requires a recovery period, not just the individual muscles. If you perform dips or pullups everyday, eventually you will wear your body out. Throw in a recovery day after every two workouts to avoid overtraining and reversing all your progress.