I don't have a HUGE collection of classic games, and some aren't even that critically acclaimed, while others are incredibly typical. I was blessed in that my parents never got rid of any of my old games, so I still have them around. I trade in a LOT of stuff that comes out today, and keep the ones I think will remain great forever. Some just remind me of times as a kid... In addition to the ones I have below, I have every Pokemon version created since Red/Blue (excluding the terrible spin-offs) for their original system. I also am not going to list the other handheld games I have kept. Too many! Listed are the games I will never get rid of, even though I don't actually have the system to play some of them...
NES
-Super Mario Bros./ Duck Hunt duo-cartridge
-Dr. Mario
-Super Mario Bros. 3
Genesis
-ToeJam & Earl
-James Pond 3
-Double Dragon
-Sonic the Hedgehog
-Joe & Mac
-Spider-man
-Meximum Carnage
-X-Men
SNES
-Super Mario All-Stars
-Yoshi's Island
-Donkey Kong Country
-Final Fantasy III
-Super Mario Kart
-Chrono Trigger
N64
-WrestleMania 200
-WWF No Mercy
-Pokemon Stadium
-Pokemon Stadium 2
-Pokemon Snap
-007 GoldenEye
-Super Mario 64
-Star Fox 64
-Diddy Kong Racing
-Star Wars: Shadows of the Empire
-Majora's Mask
-Super Smash Bros.
PSOne
-In the Hunt (original over-sized hardcase)
-Final Fantasy VII
-Legend of the Dragoon
-WWF Smackdown
-Tekken 2
-Tony Hawk's Pro Skater 2
-Crash Bandicoot
-Ape Escape
-Grid Runner
Misc. Modern Games
-Final Fantasy X (PS2)
-Final Fantasy XII - Special Edition Metal Case (PS2)
-Morrowind (XBox)
-Skyrim (PS3)
-Dark Souls (PS3)
-Windwaker (GC)
-Super Smash Bros. Brawl (Wii)
-Super Smash Bros. Melee (GC)
-Halo 2 (XBox)
-Halo: Reach (360)
-Kingdom Hearts (PS2)
-Smackdown!: Here Comes the Pain (PS2)
I know the question was "which games do we cherish?" I'd like to say all of them, but if it came between these games and killing a baby... Eh? Coin flip... Gun to my head, if I had to pick three of them to take with me into the next life, I'd pick Legend of the Dragoon, Super Mario Bros. All-Stars, and WrestleMania 2000.