A lot of good recommendations have been made.
I've got a few I'd like to suggest too.
Every game should work no matter what folders (or computers) you move it to in an operating system. So say you need to move all your games on to another hard drive you can just move the entire folder containing all your games onto the other hard drive and all the games should still run properly.
It is very annoying to have to re-download or reinstall all of one's games when one installs a new hard drive and try migrating software over to it.
All games should be multiplatform, working on Windows, Mac and Linux. So all games should use something like OpenGL and not platform specific graphics software. Any additional requirements other than a modern operating system (whether Mac, Linux or Windows) should be available for all three OS and be (optionally, for those who already have it) distributed free of charge with the game.
All games should be nearly completely self contained, not requiring any pay for software/OS or any other software a user wouldn't already have installed. So games should not require: Java (though many computers have it installed), Flash (though many computers have this installed too), Steam, Impulse, Windows OS or any other kind of other software a user must install/download/pay-for to play a game.
All games should be able to be minimized, windows re-sized and full-screened.
Games should be able to be paused at ANY time, even in the middle of cut-scenes or splash screen (probably mostly for single player games). Perhaps it would be nice if cutscenes could be fastforward and reversable as well. Some times a player may miss something important in a cutscene.
All game should be mod able. Include some kind of level, stat and state editors.
All games should have some kind of cheat (perhaps unlockable?) to go to any part of the game of any level. So say you could not only enter a cheat to jump to any level of Mario, but you could also skip to any part of the level, like skip right to fighting Bowser.
Be able to back up and share save data.
Be able to load sound track onto MP3 player for listening while not playing the game.
I know some of these may not always be feasible, appropriate, practical and/or affordable, but I think some of these 'features' would be nice.