As Dan astutely points out, games that were revolutionary may not have aged very well. It's like telling a farmer that he HAS to use a John Deer steel plough from the 1880s because it TOTALLY changed how we grow corn.
I look at a lot of the games that shaped and defined my tastes and sensibilities as a gamer and it's pretty easy to find games that took the formula as inspiration and eventually did it better. If you're interested in the history of vidya, a lot of these so-called "MUST PLAY" games serve as excellent museum pieces. In the end, it's silly to hold up games from ten, twenty, and thirty years ago as definitive experiences. Outside of very rare exceptions, whatever those games do, they have been outdone at some point.
Ultimately, whatever list you concoct to answer this question speaks more to you as a gamer than any sort of objective analysis.
So, with that in mind, here are the list of games that irrevocably influenced my own experience (and the approximate year I encountered them). As it is impossible to recreate the context under which these games were experienced, I don't expect anyone to agree (hell, some of these I wouldn't even recommend, e.g. ultima III). In fact, I fully expect a lot of laughter due to the extraordinary oldness of most of the list.
Early Years
Asteroids (1985)
Pac Man (1985)
Super Mario Bros. (1987)
Metroid (1988)
RBI Baseball (1998)
Mega Man II (1988)
Bubble Bobble (1988)
Bionic Commando (1988)
Castlevania (1988)
Tetris (1989)
TMNT Arcade (1989)
Ultima III: Exodus (1990)
SimCity (1990)
Duck Tales (1990)
Double Dragon II (1990)
Curmudgeon's Golden Age of Gaming™™™™™
Chuck Yeager's Air Combat (1991)
Final Fantasy IV (1991)
Tecmo Superbowl (1991)
ActRaiser (1991)
Legend of the Mystical Ninja (1992)
A Link to the Past (1992)
Prince of Persia (1992)
Ultima Underworld: The Stygian Abyss (1992)
Dune II: The Building of a Dynasty (1992)
Wolfenstein 3D (1992)
Street Fighter II (1992)
Soul Blazer (1992)
Syndicate (1993)
King Arthur's World (1993)
Secret of Mana (1993)
Zombies Ate My Neighbors (1993)
Day of the Tentacle (1993)
SimCity 2000 (1993)
Mega Man X (1994)
TIE Fighter (1994)
EarthBound (1995)
MechWarrior 2 (1995)
Warcraft II: Tides of Darkness (1995)
Chrono Trigger (1995)
Kirby SuperStar (1996)
M.A.X. (1996)
Symphony of the Night (1997)
Multiplayer BattleTech (1998)
Slowing Down
MechCommander (1998)
Dark Age of Camelot (2002)
Hearts of Iron (2002)
Mass Effect (2007)
Mario Galaxy (2007)
Castle Crashers (2008)
Borderlands 2 (2012)
Hotline Miami (2012)
Bravely Default (2014)