Deus Ex- It's a perfect blend of FPS, stealth and RPG. The story, attention to detail and level design is simply incredible. Even Invisible War succeeds in those three aspects although it suffers from some poor game development decisions.
Any Legend of Zelda game- There is something special about the first time you play through a Zelda game.
Super Mario World- Perfect 2D platforming
Half-Life 2- Perfect single-player FPS and introduced physics as integral to gameplay. It's a part of gaming history.
Portal 1/2- Brilliant level design, script and puzzles.
An Unreal Tournament game- Fast-paced multiplayer fun that can't be beaten.
GTA V- Sandbox perfection
An Elder Scrolls or Fallout (Bethesda) game on PC with mods- There are few devs that can make a world as detailed as Bethesda manage, and fewer that can make one as big whilst maintaining that detail. And for everything else, there's mods.
Mass Effect 1, 2 & 3- There are few games that can make you actually feel something for NPC characters. The way your decisions carry through across the trilogy is something that just hasn't been done to the degree Bioware managed in this series.
A Mario Kart in multiplayer- Probably the best local multiplayer game you can play.
Planescape Torment- for story and writing alone
Metal Gear Solid series- There's something unique about Kojima's 4th wall breaking stealth series that just has to be experienced.
War Thunder in VR- War Thunder is an OK game. In VR, it's something special that just has to be played.
A Civilization game- The addictiveness has to be experienced!
Gone Home- A game that is pure storytelling and embraces the interactive environment. The story is uncovered as you make small discoveries and piece the bits together in your head. All story based games should have at least some of the aspects explored in this title.
A Final Fantasy from the SNES/PS1 era- jRPGs from this era were the pinnacle of the genre. Any of these titles should be tried for a taste of quality jRPGs.