The worst paintball hit, if you obey all the safety rules, rates about a 4. If you use all the recommended safety gear, instead of just the required stuff, you'll see a 2 at worst. If you don't use any safety gear, pain levels of 10 (followed by a swift death) are very likely.
Take a rubber band. Have someone put one end against your arm, then stretch the other end out tightly and release it. That will hurt worse than 99% of all paintball hits.
With the proper equipment and obeying all safety rules, paintball is safer to play (insurance companies actually track this sort of thing, and sometimes publish their lists) than golf. People have literally been killed playing paintball, but every single incident was due to some dumbass thinking the safety rules didn't apply to them (unfortunately, the dumbass is often not the one who dies) and there have only been a handful of fatal incidents in the almost 30 years the sport has existed (making it one of the safest sports, from a mortality rate standpoint, on Earth).
Required personal safety gear is paintball-certified goggles with ear and jaw flaps making it into a mask. One of the dumbass-accident causes is wearing other types of goggles (shop goggles, ski goggles, swim goggles, etc); Ever seen a brick thrown through a plate glass window, with all those razor-sharp blade-like shards? That's what happens to your eyes with non-paintball goggles when the lens gets hit; So get real paintball goggles.
Not in the personal category, but definitely in the required category, is a barrel cover. It looks like a little bag with a long retention cord, that fits securely over the end of your paintball gun barrel, making it incapable of shooting paintballs. Yeah, most guns have a safety, but why risk blinding someone for life in the safe zone?
Recommended personal safety gear is long sleeve shirt, denim pants, shoes with ankle support, gloves, neck gaiter, and either a chest protector (for females) or a cup (for males). You don't need any of the recommended gear, but they greatly reduce the pain level (especially chest protectors, cups and neck gaiters).
Another recommended item is nail polish. Not for the player, but for the gun. Attach the air tank (CO2, HPA, whatever) to your gun, then look down at it. Paint a line of nail polish across the seam between the regulator and the bottle neck. Every time you remove the tank from the gun, look down at the line. If the two halves of the line ever fail to line up, STOP EVERYTHING, and announce in a loud but clear voice "My valve has come loose from my tank, everybody get clear NOW!" The situation, called the Rocket Bottle problem, is a rare one, usually caused by the dumbass mistake of trying to service or modify an air tank without the proper tools, skills or knowledge. You know how in the movies, knocking the valve off a big welding or SCUBA tank can make the tank penetrate a brick wall like a rocket? The same thing can happen on a smaller scale with paintball air tanks, and if it hits anyone, they'll probably die. People have died of this in the past, but every single documented incident was the fault of a dumbass who violated both safety rules and federal laws to make it possible. A similar precaution is to tuck the tank under your arm while detaching it (and make sure nobody is behind you as you do this) so if it does go flying, you're not between it and freedom.
As other posters have noted, the most common paintball injuries are ring or disk welts (depending on how the ball hits) and bruises. I've also seen paintballs draw blood (minor bleeding), break or tear off finger nails (this is why gloves are recommended), and once I saw a guy lose consciousness from shock after a groin hit (he was only out for a few seconds, but this is why cups are nifty). The more extreme injuries are quite rare, and wearing the recommended safety gear reduces them to trivial concerns at worst.
The last type of injury you sometimes see, and typically the worst (short of outright death), is eye damage. This is always the result of dumbassery. Either someone used non-certified goggles, or lifted their mask while in the hot zone, or some dumbass fired off a shot in the safe zone (which is why everybody must have a barrel cover). A paintball, even a the lower muzzle velocities you see at indoor fields, will pop an eyeball with ease. Permanent blindness is the most common result of this. So don't be a dumbass, and don't tolerate others being dumbasses around you.
12 years of paintball playing experience, amateur airsmith.