I think the main things you have to identify for this are which games have been the most important for the development of games in general and in the way that those games have helped to define the gaming landscape. For this reason I pick:
Half-Life: The most influential and important first person shooter ever made in my opinion. The focus upon immersion by keeping the player rooted into Gordon Freeman's perspective combined with intelligent AI and tight scripting has resulted in some of the finest moments available in gaming today. Bioshock, System Shock 2, Call Of Duty (Any of them), Halo and Half-Life's equally important sequel wouldn't be here today if it wasn't for Half-Life. That alone merits its inclusion.
Command And Conquer: And yes, before anyone starts yelling, Dune 2 did RTS first. But it was Command And Conquer that took all of the elements from Dune and stuck them into a finely balanced world with an easy to sue interface. Dune may have created the architecture, but Command And Conquer consolidated the RTS genre into one of the biggest genre in gaming. Is Starcraft superior? Yes. Is it as important? No.
Super Mario Bros: Nothing can be said about Super Mario Bros that hasn't already been said before. It's one of the most important games in video game history, and still plays as well as it did when it was first created. It's one of the pinnacles of platforming design and is THE platforming game that established the genre, helping to define gaming's identity in the 80s and 90s.
You really can't have only 3, but if you were going to have 3, those would be the ones to pick. I'd love to have a role-playing game in there since they seem to be more popular than RTS games just now, but that's the way the cookie crumbles. I think that the creation of a brand new genre that can ONLY be played upon consoles and computers is far more important than an evolution of pen and paper role playing, which the RPG has developed out of.
And it really, really bugs me that I can't stick System Shock 2 in there but Half-Life's more important. I think these three cover three core elements of gaming that are still seen today: technical skill and purity in Mario, the development of story telling in Half-Life and strategy and intelligence in C&C.