Impending Doom POV

Probably the most common use of POV Cam. These are camera shots of the heroes from an angle that obviously is someone's point of view, presumably a stealthy attacker. To ensure that the audience realizes this, the shot is often taken at a strange angle, through shrubbery or shelving or some other form of cover. Also, we can frequently hear the attacker breathing. But the hero remains oblivious.

Film

Subverted in Indiana Jones and the Kingdom of the Crystal Skull, where Indy and Mutt are in a tomb, shot from what seem to be assailant's POVs, but no one attacks.
- Similar use in Red Eye, to trick us into thinking the bad guy is hiding in the shower.
Hollow Man, though the assailant is the main character.
Jaws, of course.
Predator, combined with different visor.
Evil Dead, with the magic of Shaky POV Cam.
- Forever Evil did this one too, ad nauseam.
A number of classic slasher movies used this, most notably the Halloween movies (complete with Vader Breath) and the original Black Christmas.
Kingdom of the Spiders gives the viewer Tarantula-Vision.
Snakes on a Plane uses a bunch of distorted green-monochrome shots to represent the snakes' rather poor eyesight.

Live-Action TV

A favourite of Doctor Who, particularly the old series, as a way of delaying the expensive and possibly slightly naff creature shots until later in the story.
Before we saw Lost's smoke monster, we saw its POV looking at Locke and Eko.
Back in the 80's, USA Network had a weekend movie host named Commander USA. During an airing of the film Monster in the Closet, he starts to discuss this technique, and the camera shot cuts to a POV of someone sneaking up behind him with a large knife. But then the Commander makes some comment to the effect "but often, it's all just a big fake-out and nothing actually happens", and the knife-wielder promptly vanishes.
If you're watching Stargate SG-1 and you see one of these shots through the cover of bushes and leaves, chances are there's a lurking Unas.

Video Games

The third Rayman game has one of the few uses of this in gameplay that is not a Jaws First Person Perspective. Enter the wrong rooms in a particular mansion, and you'll see through the crosshairs of the owner's gun, with only a few seconds to duck behind furniture.
Used in the Left 4 Dead intro when we see Louis through a hunter's eyes. Notably, the game creators changed the cut scene to use this trick to make the attack on Louis seem scary, when it'd previously been comedic. It worked.
Throw an enemy onto the subway tracks in Def Jam: Fight For New York, and the last thing before the Gory Discretion Shot is their look of panic as the train comes down.
Mech Warrior 3. During the intro the view shifts to being in one of the LRM's launched from Lance Leader's Mad Dog as they strike a Summoner Mech's cockpit.
In Call of Cthulhu: Dark Corners of the Earth, the protagonist's psychic powers occasionally kick in; sometimes, this results in the player seeing through the eyes of an incoming monster.
During Madison's dream sequence in Heavy Rain, there are several shots like this, particularly if you have her take a shower.
In Kingdom Hearts: Birth By Sleep, the Unknown Heartless (AKA Red Eyes) stalks Aqua in the realm of darkness in this manner. It even does this during the first phase of the battle, and the player must use the POV to avoid its attacks.
The boss Crayk's POV in Phantom Hourglass is shown on the upper screen of the Nintendo DS.

Web Original

Stickdeath.com^{[dead link]} has two early flash videos using this technique, based on the famous "Missile-Cam" technology; one, titled S.A.M., depicted the missile homing in on someone sitting on the John, while the other, title F.A.D., for Final Act of Defiance, has the unlucky target giving the missile double deuces.

Western Animation

Spoofed in Monsters vs. Aliens: the "attacker" is really Susan's bridesmaids waking her up on her wedding day (The scary breathing we hear? One needs an inhaler).