My favorite game of all time is definitely Starcraft. However, I personally do not believe that Starcraft was all that important in the gaming world in the States. Obviously it revolutionized gaming as a sport throughout the world, but not so much here.
I have played almost every "Greatest Hit" that has been made from NES to Xbox 360. I have still yet to play a PS3, because I know that if I do, then I'll end up buying it, and I can't afford it atm. This is just a short list of the 10 that I think changed gaming for me.
1) Super Mario Bros. - This is the Mecca of the gaming world. The game that put games in the hands of EVERYONE. It was also the first game I ever played. I beat it in a week after lots of failing because my NES was a piece of shit.
2) Halo - Now, don't shoot me for this one. This is arguably the best mixture of Story, Gameplay, and Replayabiility that was available at its release. It also helped put Microsoft on the map as a competitor in the Console World.
3) Half-life 1 and 2- Personally, this is the best gaming series I have ever played. Once I start them, they keep me hooked up until the explosive endings. These games redefined the "Next-Gen" FPS, in that story is just as important as gameplay. Also helped promote Modding in large part due to the open nature of Valve's engines.
4) Starcraft - Definitely defined Blizzard and the whole RTS genre in its own right for the better part of ten years. I have played it since 2000 and have enjoyed every second of its gameplay. The sheer perfection that was the way all the races were balance but completely different and how there were ALWAYS new strategies to learn and explore. No doubt this is an important game in that its influence has changed the way companies go about creating their games. Innovation is KEY.
5) Wii Sports - Now, don't shoot me. This seems odd, I know, but, this is the game that comes with the Wii. It's the game that instantly acquaints you to the simple use of the Wii Remote and all of its possibilities. Plus, who has never played this game?? Good luck finding someone who hasn't.
6) World of Warcraft - Well, I only played it for a little while. I got a Tauren Shaman to level 43, but quickly ran out of income and time, and had to let it go before I lost any chance at career as a musician. The ultimate time-suck. People literally live and die based on this game. Has found a way to get a novel concept and make it accessible to EVERYONE. Millions are still grinding away in the many dungeons to find the perfect drop to finish out their gear. Oh, and they are still making VERY successful expansions for this monster-grossing game.
7) Madden 96(I think this is the one) - This finally made a sports game that people could easily pick up and enjoy. Set the bar for future sports games in every sport. It also introduced a yearly development cycle that feeds to the ultimate football fans that enjoy being up-to-date with their sport in its playerbase and in its Madden features. Add Franchise and Superstar down the road, and internet play, and this game is STILL selling Millions of copies even with its yearly release.

Call of Duty - Great Game. Top 5 FPS of all time. Would have to say that this is one of the first games that REALLY was accepted as a tournament video game. Hugely known for its great single player story and flow, but now is more known for the millions that play online everyday on various consoles and versions. Also has taken the whole yearly release flow.
9) Guitar Hero - More controversy. Remember Amplitude? Well remember how bad it was? Harmonix took that concept and the desire that every teenage kid has to become a rock star and turned it into a HuGE franchise. No one can deny that they have played this (or Rock Band) at parties, totally drunk off their asses, singing a song by Evanescence is a girly voice while dancing around half-naked on a table. (Well, maybe not exactly, but you get my drift) One of my favorite games to play now. With Rock Band's introduction of new instruments other than the guitar also helped put this game on the list of every teenager in the US. Rock on, my friends.
10) Final Fantasy (the whole Franchise) - Turned story-driven gameplay upside-down and made it enjoyable. I remember spending hours trying to reach Sephiroth, only to find out I was too late to save my friend. Fantastic games made even better wtih fantastic music and visuals that created a fantasy world I wished I could be a part of.
This is just my view of the gaming world and its footholds. There's so much more I could add on so many levels, but I just don't feel like typing anymore.