You said it Homer. Also, Emanuel Lasker also said as much in his florid intellectual style:

"On the Chessboard lies and hypocrisy do not survive long. The creative combination lays bare the presumption of a lie; the merciless fact, culminating in a checkmate, contradicts the hypocrite."

Most of the games that are my favourites are flawed in some way. Even when they came out. Planescape has imperfect combat, Deus Ex weak AI, Bioshock is too linear, Final Fantasy 7 has too few savepoints in part...

In that case, those eternally unchangeable perfect games would be indeed, as someone mentioned, Solitaire and Minesweeper...

But there are times, when games are released, that AT THAT VERY MOMENT are perfect. You play them, and you wouldn't change a thing. Of course, a few years later you may want the graphics updated, the control scheme doesn't support the possibilities of your modern controller, the resolution, while fine on a 15" CRT will look incredibily blocky on a 24" LCD. The difficulty was perfect just then, but now you're older and don't have the reflexes anymore but instead wife and kids that distract you and break the flow - so you wish for "save anytime". Or an automapping feature and quest log.

Some games that were perfect at their time were:

Single player:
Katakis/Denaris (C64-version)
Turrican 2 (Amiga-version)
Apydia
Doom 1+2
Civilization 1+2
Master of Magic
Master of Orion 2
Dungeon Master
Ultima Underworld
Monkey Island 1+2
Indiana Jones 4
Pirates
Test Drive 2
The Need for Speed
Death Gate
Final Fantasy 7
Sim City (not C64).
Return to Castle Wolfenstein

Multiplayer
Doom 1+2
Quake 1+3
Battlefield 1942
WoW

John Carmack doesn't think so.

Who cares if someone plays it and doesn't like it?

"Perfect" doesn't mean a game that every gamer loves. A perfect game IMO is 1. a game that is the ultimate example of its genre (one that is upheld as being a "classic" or the "daddy" of <insert genre name here>) and 2. is totally flawless (in that the fans of that game wouldn't change a thing about it).

BTW I recently finished PW: AA. It is a near-perfect non-dating visual novel game. I enjoyed it. But there is still something I would change about it:
How do you like the sound of unlocking a music player and a picture & credits viewer upon beating the game? :)

(Also - and this is probably just me but - I found the last case spoiled the over-all storyline IMO. It felt tacked on. This case wasn't part of the original Japanese GBA game - it was "ret-conned" years later into the DS release).

Well, by that extreme (although precise) definition or perfection (no element changed) no videogames could be considered perfect. I mean, what game could not be better with a few lines voiced by John St John? Or better graphics if one cares for those things.

There are probably perfect games becase they define themselves their own formal rules and are only defined by them, like chess or poker, but obviously you were not asking about that and many people find those games boring and a perfect videogame should never be boring. So... although it probably says more about me than about the games, mmh... HoMM3 is close enough, Baldur's gate (very few improvements necessary, really), Half Life (it needs a few graphical improvements, but for me it is a minor issue), Deus Ex, Starcraft (never enjoyed it very much, but it is a very good game)... and probably more. Oh, and psychonauts, yes.

Well, I have 98 days and 3 hours of /played in WoW, so I guess that would make it the perfect game for me? Can one even call a game perfect?

The Longest Journey
Mass Effect
Planescape Torment

All three contains everything I wanted to experience in games. Strong focus on story, huge lore, challenging moments, unique atmosphere of unknown worlds, full of "breathing" characters, joy to play from the beginning to the end. Each of them has flaws but I think of word "perfect" as a right combination of strengthes and weaknesses.

If you mean perfect as in you can't stop playing even if you want - probably The Guild. Rules are clearly set, there are always many things going on and thus it doesn't feel hollow, literally infinite gameplay. I reinstall it from time to time and always got stuck playing it for hours.

Yep. I have. Ultima 7

Yes, it is called Super Metroid.

Well, it's certainly not the only thing he's been wrong about

The perfect game? If there would one i would only playing that. So no i've not played
a perfect game.
If you count the time playing a game....it would be Ultima Online. I played it from
1997 till 2005/2006. But it wasn't perfect.

Civilization II was as perfect as a game got for me. I loved the first one but when the second game came out, they had impoved everything within the game. I played it forever, until Civ IV: BtS.
Many of the old Microprose/Sid Meier's games were fantastic - MoM, Alpha Centauri, MOO, etc. They were my favorite company back then.
Warlords was pretty dang awesom too but haven't played it in over 20 years so maybe thats my young mind talking.
Can't think of any games in the past 10-15 years that I can put on this list - don't make games like they used to.

All the people voting for Planescape Torment must have a much higher tolerance for major bugs (yes, they were eventually patched) and uninteresting combat then I do.

For me, a perfect game would have to be something casual like Tetris; no room for flaws to creep in because it's so fundamentally simple.

Not perfect, but close: Heroes of Might and Magic 3 The Shadow of Death.

Yes. Fallout, Fallout 2(after patches, of course), Close Combat 3, original Day Of Defeat, Diablo and Baldur's Gate 2.