Hmm im going to agree with some of Fraggles games
Doom is a awesome game, with awesome gameplay and storyline
C&C is good too, but storyline jumps from game to game
Halo of course, good storyline, and would make a great new game based around it. Might wanna also read the books too!
Gears of War 1 and 2 are good choices if your looking for a shooter style.
Neverwinter Knights has a VERY in-depth storyline, with lots of lore in the game plus item making, spells, and swordfighting.
Starcraft of course! Storyline kinda starts in the middle, but if you read the books, you understand it well
If you want a turn based game, take a look at Civilzation and Galactic Civs. Very good turn based games.
If you want a good medevil/fantasy game look at the Elder Scrolls series. Good games, and good graphics.
If you want a RTS space game, look at Sins of a Solar Empire, good game, graphics, and controls are very easy to learn
If you want more of a older game feel, look at Warcraft III, custom games are makeable, and mapping is easy and fast if you like that stuff.
Lastly, for a Tycoon style game, look at Rolercoaster tycoon, or Zoo Tycoon 1 and 2.
That should cover most game types, hope this helps!