If You Were Tasked To Provide Someone With The Experience Of Video Games?

Rpg - final fantasy 6, 7, baldur's gate 2, fallout
Rts - Starcraft, age of empires 2
Fps - perfect dark, goldeneye
Platform - symphony of the night, God of war
Puzzle - Tetris, lumines
Survival horror - fatal frame, resident evil 4
Driving - gran turismo 3
Sports - ssx (the one for the ps2 not that remake atrocity)
Action adventure - Diablo 2, ocarina of time
Stealth - metal gear solid
Third person shooter - gears of war

If you want someone to experience the video game experience why wouldn't you pick the best that each genre has to offer. You don't want them playing something like pac-man for the Atari 2600.

To give the full experience, I'd start old school with Pac-man, Intellivision Baseball, and Super Mario Brothers.
Next, I'd offer Sonic2, Kolonoa, and Kolonoa2. Metal Gear Solid, Ratchet and Clank, and Kingsley's Adventure.

Ridiculous… 20 games?
You only have three types of games, and variations of the three.
Exploration/ Puzzle, Rut, and shooters.
"Skyrim" is an excellent example of the three. Along with "GTA: San Andreas" and their open world ilk.
Then you might consider Rut games, where you have to stay in a single linear path with no or very little movement out side of the Rut. Games like "Call of Duty", "Assassins Creed", and "Just Cause". Ruts are also race games where you are confined to a roadway or race track.

Super Mario 64
Uncharted 2
Assassin's Creed 2
Super Mario Sunshine
Tetris (this will get them hooked)
Legends of Zelda Wind waker
Infamous Second Son
Dying Light
Sims 3
TF2
The Simpsons Hit and Run
Portal 1&2
Little Big Planet 2
House of The Dead 2

That's all I got

20 video games to get a good experience?

1. Pokemon (Gameboy)
2. Mario Party (1-9 Any system)
3. Mario Kart Double Dash (Gamecube)
4. Legend of Zelda: Majora's Mask (Nintendo 64)
5. Mortal Kombat (Super Nintendo & XBox)
6. Sonic Riders (Gamecube)
7. Scribblenaughts (Wii U)
8. Super Smash Bros (1st, Melee, Brawl, or Smash4)
9. Super Mario 64 (Nintendo 64)
10. Super Mario Galaxy (Wii)
11. League of Legends (PC)
12. Diablo 3 (PC)
13. Starcraft 2 (PC)
14. Soul Calibur 2 (Gamecube)
15. Plant Vs Zombies (Smartphone App)
16. Warframe (PC)
17. Fable 3 (Xbox)
18. Minecraft (Xbox)
19. Rayman Battle Arena (PS3)
20. Injustice (WiiU)