Pull-ups are far and away the best exercise for your upper body because they force you to literally pull your own weight.
Pull-ups are a compound multi-joint exercise that develop physical fitness and functional strength. They protect and strengthen your shoulder girdle and build all the muscles of the back which boosts your metabolism.
To fully train and exhaust the latissimus dorsi, trapezius, and rhomboids it's imperative to train the back with wide grip pull-ups with the palms facing away from your body and also narrow grip pull-ups with your palms facing your body (narrow grip pull-ups are sometimes called "chins" or "chin-ups").
There is a strong correlation between the number of pull-ups a person can complete in single set and their overall health and fitness. This is because a person's max pull-ups are primarily a function of two factors, pulling strength & endurance and body weight. Obviously, a person with a healthy weight has a huge advantage over an overweight or obese person, they simply don't have to pull-up as much weight.
Furthermore, pull-ups serve to correct muscle imbalances and improve posture. Most people will naturally (or unnaturally) develop stronger "push muscles" in the upper body. Pull-ups obviously develop the "pull muscles" and therefore can help eliminate muscle imbalances and improve posture. In general, you should be able to perform approximately one third as many body weight pull-ups as body weight push-ups. Ergo, a man that can do a max-set of 30 body weight push-ups should be able to do roughly 10 body weight pull-ups.
However, all adult males 18-39 should be able to do roughly 20 body weight pull-ups. If you're a part of this demographic and can't do roughly 20 pull-ups, than for your own sake, you should make that your goal and start working towards it. You will need to BURN FAT (some people say "lose weight" but that term is far too general) and get stronger. As an added corollary you should be able to perform 50-60 push-ups, remember the 3:1 ration.
If you can far and away exceed 20 pull-ups (like 30+) then you probably need to BUILD MORE MUSCLE (some people would say "gain weight" but again that term is too generic). I recommend going to the gym, locating the squat rack and building bigger, stronger, more powerful legs.
Women, the body of goddess will naturally follow an increase in the number of pull-ups you can do. A woman that can do 10 pull-ups will have a lean, strong and sexy body. Unfortunately, some institutions like the United States Marine Corps, rob women of the opportunity to be tested on and improve their pull-ups. Instead they substitute the "Flexed-Arm Hang" which is a totally bogus non-exercise. Women, do pull-ups! Set a goal to do 10 pull-ups and 25-30 push-ups (remember the 3:1 ratio) and don't let anyone or anything stop you.
Q: WHAT IF I CAN'T DO A PULL-UP? HOW DO I GET BETTER?
A: 1. BURN FAT, run, walk, play sports, shovel snow, go for a hike or bike ride and most importantly, EAT RIGHT!
2. GET STRONGER, you can work your way up to body weight pull-ups by having a spotter hold your feet while you perform "less than body weight pull-ups." You can also use a Lat-Pull-down machine to perform wide and narrow grip pull-downs to build strength.
To totally transform your body and improve at everything, including pull-ups, You should get the TSC Heart of a Champion Training & Nutrition Program and start training and eating properly immediately, for your own sake.