I've been thinking about game design lately, and it occurred to me that I never evaluated games in the same way I often evaluate books and movies and music. That is, I never ask myself what games am I glad I played. I mean what games do I value beyond the momentary entertainment value that, afterwards, I acknowledge as really worth my time. I mean how an action flick you can enjoy watching, but really you don't care about it after it's done with versus a good movie that leaves an impression.

So then it occurred to me that there were really no games that I value like that, with the possible exception of Earthbound, but that's stretching it a little bit, I think. Chrono Trigger, the Final Fantasy series, Zelda, I'm not really glad I've played any of them except for nostalgia sources... I think so, at least.

So, what games are you glad you've played?

Off the top of my head:

Doukutsu Monogatari (Cave Story)
Final Fantasy 6 & 9
Okami
Tales of Symphonia
Commander Keen
Nethack/ADOM
Collosal Cave/Zork
Monkey Island 1 & 2
Legend of Zelda: Windwaker

Some of these I'm more glad that I played them because of influence on me - Commander Keen, ADOM, and Collosal Cave were huge influences and, I suspect, are large parts of the reason that I decided that I wanted to make games.

Ack! I can't believe I forgot (I was reminded by Overkill's list):

Shadows of the Collosus
The Legend of Zelda: Links Awakening

Final Fantasy 6
Chrono Trigger
Secret of Mana
Breath of Fire 4
Suikoden 2

Twilight. Princess.

Maybe I'm overhyping it, but I enjoy it immensely so far. It's like...Ocarina...with the art style reminiscent of Shadow of the Colossus.

*pops in head*

Here's a list:
Cave Story // I freakin' love this game =_=
Seiken Densetsu 3 // Multiplayer... with friend... amazing...
Legend of Mana // Same as above
Saga Frontier 2 // Challenging and addicting
Mario 64 // The huge crazy environment, man...
Super Smash Bros. (+Melee) // I play this too much
Halo // Atmosphere, atmosphere, this is one shooter I play too much as well
Tales of Phantasia // Not very challenging, but VERY awesome battle system and a nice storyline as well
Star Ocean: Second Story // This one's for the battle system :/
Super Smash TV // NOSTALGIA
Tales of Destiny 2 // ...MULTIPLAYER
CastleVania: Harmony of Dissonance // This. Is. One. Freaking. Amazing. Platforming. OMG!
CastleVania: Aria of Sorrow // You don't need rave reviews
CastleVania: Dawn of Sorrow // To appreciate this awesome!
CastleVania: Symphony of the Night // This is one of the only platformers I consider to be near perfect, but the translation is crappy :/
Valkyrie Profile // crazy crazy CRAZY battle system. Those folks at tri-Ace Know What They're Doing! (tm) The story is amazing, and the design and flow... the challenge... just play this. It's worth it.
Street Fighter Alpha 3 // ahhh... memories... you know, I was a fighter junky once...
DarkStalkers 3 // and this is one of the greatest fighters E.VER.
Ninja Gaiden (nes) // RYYYYYUUUUUUU
Megaman 1-6 // Just... love at first sight. The first gaming experiences I had as a child.... yeah. Addiction. 5 was my favorite.
Zelda: Links Awakening // great fun
Zelda: Ocarina of Time // I grew to love this
Gundam Wing: Endless Duel // Another great fighter... hey, I was a junky!
Dragon Ball Z: Hyper Dimension // OK OK, last fighter...
Super Mario Bros. 3 // ADDICTION!

I never really left this place, it's too great a community ;D. Just never logged one. :P

Games I genuinely care about:

Knights of the Old Republic (stunningly brilliant characterisation, particularly Bastilla)
Baldur's Gate 1 & 2 (characterisation, again. Plus the sheer size and depth of the locations the games take place in)
Hostile Waters (fun characters and a truly tear-jerking ending. Play it for me, will you?)
Deus Ex (choices that have interesting consequences)
Original War (RTS everybody ignored. Hard, but utterly brilliant. Every trooper is a character, base building is much more true to life and you get to make campaign-altering decisions throughout)
Thief 1, 2, 3 (the best player character of all time. Cynical, arrogant and completely brilliant)

The end of KotOR made me cry. Mind you, I just finished watching the whole of Bablyon 5 on DVD (missed out the first time. It's utterly fantastic) and the end to that reduced me to a sobbing wreck. So, for me to care we have to have fantastic characters in a coherent setting experiencing the whole range of human emotion. Then I'm happy.

in order of care factor -

The Legend of Zelda
Ultima 6
Kings Quest 3
FF3
Castlevania (the original)
Windwaker
Supermario Sunshine

I have recently finished Earthbound.
...
AMAZING game!

In response to the original question, I don't think there are any games like that for me. But, there are no books or movies that are that way for me either. Well, not fiction anyway. (The Selfish Gene comes most forefront to my mind as a worthwhile read). I learned a little bit from some Koei games, like Genghis Khan and Romance of the 3 Kingdoms. So I guess that's kind of worthwhile.

Anything else are just games I really enjoyed, which I'd rather have not played, because then I could play them now as a new experience. And the same thing goes for great movies or books.