Well, for me perfect would be games that were just that well designed and executed or that really pushed gaming possibilities (which often means poor sellers of course!)... so with that the games I'd have on a desert island are:
Doom / Doom 2
Half Life / Half Life 2
System Shock / System Shock 2
Deus Ex
Grim Fandango
Ultima Underworld 2
Ico
Shadow of the Colossus
Portal
It's not perfect, but if I had to pick some online games it would be:
Alien vs Predator 2 Survivor mode - my favorite online mode ever
Unreal XMP - complex, team based, goal based online... just right for me
Honorable mentions...
COD, COD2 and COD4
Jak and Daxter & Uncharted (love the lack of 'levels' in their approach)
Morrowind & Oblivion
Splinter Cell & MGS series
Mainly PC orientated as that was my primary platform for a long time... and I guess its obvious I'm looking forward to whatever Team Ico do next...
Try to be reasonable... its easier than you think...
