In chess, as in other games that promote gamesmanship, "The Stare" is a common tactic used by players to intimidate, annoy, confuse and otherwise put an opponant out of his or her comfort zone. It is generally done when a player is trying to think, and his clock is winding down, his opponant will stare directly into the eyes of his opponant.
Mikhail Tal the Eighth World Chess Champion was famous for his intimidating stare. People suggested his stare was hypnotic and that in this way the "Magician from Riga" was enchanting his opponants and lulling them into losing. Coupled with his attacking genius and fantastic calculating ability, Tal was certainly very fearsome on the board, and in this way played "the man" as well as the board. Pal Benko famously tried to wear glasses during a game versus Tal to avoid his gaze.
See video here
The stare can also be used to good effect BEFORE the start of the game, as an intimidation tactic. In general the stare is looked down upon, but rules prohibiting are hard to enforce or non-existant in most tournaments.
In Dominic Lawson's esteemed "The Inner Game" regarding GM's Nigel Short and Garry Kasparov's World Championship Match the GM Short describes in detail the "stares" of Kasparov and Karpov and supports the claim that this is a common tactic even at the highest levels of chess, and that strong players even have variations on how they do it.