In most movies the superhero escapes certain death by simply jumping into water, but would that actually save him from someone shooting at him? The answer is yes and no.
It depends on the bullet, and how fast it goes. Paradoxically, the slower the bullet, the deeper it can go. The reason for this is because of the force at which it hits the water. If it hits hard enough, the bullet will shatter and become harmless, but if it is going slow enough it will continue through the water at speeds fast enough to penetrate human flesh.
Supersonic bullets, up to .50-caliber, disintegrate in less than three feet of water, while pistol rounds need up to eight feet to become non lethal. Shotguns slugs require even deeper water.
While these are the technical measurements, in most actual situations the bullet would enter the water at and angle, reducing the amount of water necessary to make it non-lethal.
Check out the full report that Mythbusters did on this here.