Quake 3 is an online FPS from Id Software and Activision. In a departure from its predecessors, it completely lacks a traditional singleplayer campaign, and the emphasis is mostly on deathmatch.

Half-Life 2 is an FPS from Valve Software, and was one of the most highly anticipated sequels of all time. You return as Gordon Freeman, the strong and silent-type physicist, and you must do battle with an alien race of enslavers to liberate the surviving remainder of humanity on earth.
Also applies to Half-Life 2 Lost Coast free downloadable level.

Unreal Tournament is an online FPS from Epic Games and GT Software. Its main competition being Quake 3, it distinguishes itself from the Quake games by focusing on team-based games such as team deathmatch, capture the flag, and assault, rather than free-for-all deathmatch.

Deus Ex is an FPS/RPG hybrid from Ion Storm and Eidos Interactive. It is most notable for its free-form skill-based gameplay, which allows nearly unlimited solutions to missions, often allows for multiple outcomes, and lets you shape your character to be best suited for your style of play by allowing you to develop the skills of your choice.

Half-Life is the groundbreaking FPS that follows the "everyman" hero Gordon Freeman. This is the first installment of the ongoing series, which ties together aliens and government conspiracies. Really, this game doesn't need any introduction...

The Chronicles of Riddick: Escape from Butcher Bay is an FPS from Starbreeze Studios and Vivendi Universal. The plot serves as a prequel to the 2000 film Pitch Black, and features Vin Diesel's voice and likeness.

Call of Duty is a WW2 themed FPS from Infinity Ward and Activision. The game is played over three campaigns; American, British, and Russian, and most of the missions emphasize fighting as a company over lone wolf tactics.

Black & White 2 is a strategy game from Lionhead and EA. Like the original, you play as a benevolent or malevolent god, though there's less godly competition this time around. You build cities, conquer lands, and generally make your presence felt using whatever divine methods you like.

Age of Empires III is the latest entry in the empire-building RTS series from Ensemble and Microsoft. The game is set in colonial America, and covers its colonization and eventual independence, from 1500AD to 1850AD.

Set in post-WWII New York City, The Godfather: The Game follows the player-created character's rise through a crime syndicate based on the book and film franchises. Combining events from the movie with side-story missions, the player must earn respect by completing missions in territories controlled by New York's five crime families.