Catching a bullet as it flies through the air is a tired old illusion—but can it actually be done in real life? Surprisingly, yes—at least, theoretically.
A bullet fired straight up would eventually reach a maximum height. It probably wouldn't stop completely; more likely, it would be drifting sideways at a couple meters per second. At that speed, as long as you were in the right place at the right time, you could snatch it out of the air.
He suggests—well, actually he suggests against, but at least points out that it would work—using a hot air balloon to gain enough altitude without disrupting the air through which the bullet would travel. Altitude would, of course, vary as a function of the gun and bullet, but an AK-47 would require you to be 1.3 miles up in the air.
Interestingly, while the bullet would lose all it's vertical momentum, the rotational momentum supplied by the spiral of the gun's barrel would mean that it was still spinning when you caught it. Not that should try, obviously. [What If?]
Image by Sheree (Here intermittently) under Creative Commons license