My approach to this: I thought of ten basic characteristics that I appreciate in a general sense, and then chose ten games that I consider to embody each one with the least amount of obstruction. These aren't my favorite games, but in my mind playing them all will give you a better sense of what I like about the medium than playing ten that do everything listed here decently.

Just missed the cut:
Elite Beat Agents (pure instinct #2)
Kentucky Route Zero (pure storymaking)
Rain World (pure struggle)
Dark Souls (pure immersion)
Mother (pure adventure #2)
Cave Story (pure atmosphere #2)
Resident Evil 4 (pure elegance)
Super Smash Bros. Melee (pure intrigue #2)
Bayonetta (pure swag #2)
Pokemon Red & Blue (pure sociability)