The StarCraft Anthology

You can now experience the game that put Blizzard on the map for free. Legendary real time strategy game StarCraft has been remastered (bug fixes and slight graphical updates) and re-released for free.
The Starcraft Anthology has been updated to work with all modern operating systems and has a fairly large playerbase. The game stands the test of time and is still one of the best strategy games of all time.
Wolfenstein 3D

Wolfenstein is a classic- this game is one of the first FPS titles to be released, and it almost single-handedly created a new genre. Although the graphics are incredibly dated, the game is still quite fun to play (and is a HUGE piece of gaming history).
The fast paced, run and gun style gameplay holds up well, even in the era of modern shooters like Call of Duty and Battlefield.
Tribes

Credit: Hi-Rez Studios
The entire Tribes series is available for free now. Tribes is a first person online shooter that differs from your normal, reality restricted FPS. The series is known for excellent level design and use of items like jetpacks and some very creative weapons.
The gameplay is fast, complex, and incredibly fun. There are many games in the series, and even the newest title is free to play.
The Marathon Trilogy

The Marathon trilogy set the standard for sci-fi first person shooters for years to come after its release. The series debuted now-common FPS features like dual wielding and some of the multiplayer modes introduced by the series are regulars in modern FPS games.
However, beside the innovations brought to the table by Marathon, the games are best known for their incredible storytelling. A story as big, complex, and intriguing as Marathons had never before been seen in an FPS.