A supporting character in many video games for various Nintendo systems set in the Super Mario Bros. universe. It is in the form of a white ghost with a sadistic grin on its face.
In their simplest form (in action, side-scrolling, or platform games), Boos slowly sneak up on Mario (or another protagonist) and either cause damage or kill the player's avatar on contact. They turn transparent (and usually become immune to damage) when faced down directly. In side scrollers like Super Mario World, this effectively rendered them invincible, since technically one could kill them by jumping on their heads, but could not do this while the ghost is solid (and hittable), as turning around to line up the attack would turn it transparent (and they always face you, so can't be snuck up on). In more recent games, like Super Mario 64, they wander freely in the 3D environment and can be pounced when they're not looking.
Outside of platform games, Boos have served ancillary purposes in games such as the Mario Party series, where Boos can be bribed to steal other player's coins or stars.
While they were silent in their first appearance in games, in later incarnations, their trademark noise became a high-pitched, echo-filled cackle. "Normal" Boos are somewhat small, rarely matching the size of an adult human (think Mario here). "Big Boos" are exactly what their name implies -- very big versions of normal Boos. These tend to be stronger, and usually immune to normal attacks. In some instances they're a major nuisance, but in others (such as in Super Mario Sunshine), they're just in the way and don't actually attack anything.
Early on, these were sometimes called Boo Buddies, but the 'Buddy' part of the name was dropped, mostly because they certainly werne't anybody's "buddy".
Boos are known to have appeared in at least these games:
There are probably others (please /msg me if you have an addition or correction to this list).
RPGeek points out they also appeared in Super Mario Brothers 3 and Luigi's Mansion. Servo5678 also mentioned SMB3, and adds Super Mario Kart, Mario Golf: Toadstool Tour, Mario Tennis, and the Super Mario Advance games to the list. He also points out they originally held the moniker of "Boo Buddy". generic-man adds Super Mario Bros. DX for Game Boy Color (they were part of a mini-game). Thanks, guys!