An enemy, sometimes referred to as monsters or bad guys (or mobs in the case of MMO players) is any sort of computer-controlled NPC or entity that tries to harm the player. In many games, the common enemies are almost as recognizable and iconic of the series they appear in as the main characters, such as Goombas from the Mario franchise or Metroids from the Metroid series.
Enemies often drop power-ups upon defeat, or may reward the player with currency and/or experience points. Enemies can be thought of as a tool used by developers to keep the game going, and to pace out levels between boss fights.
As games advance, enemies are becoming more and more involved in the gameplay. For example, in The Legend of Zelda: The Wind Waker, Link could steal weapons from enemies, and lure them away with bait. In Eternal Darkness: Sanity's Requiem, enemies could be 'hijacked' with magic and used to complete physical puzzles that would be otherwise fatal to the player. In Metal Gear Solid and some similar stealth-type games, the focus is not on attacking enemies head-on, but rather sneaking around them (or eliminating them in a covert manner).