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You can play Doom or similar games if you remap the keys. Some games of that type may need a source port to let you remap the keys.
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Maxxer: I just remembered that too, I have it on my GOG shelf :D
That should keep you occupied for a sufficient amount of time ;)
http://www.oneswitch.org.uk/IMAGES/1/dragonplus-one-handed-controller.jpg

Heh.
You only need the arrow keys for Tyrian and Flatout (except on the menus, I don't remember). They're both arcadey, no story whatsoever, time killer games though.
I think you're gonna have to go turn-based. I don't see a lot of games on my desktop which can be played with just the off-hand, and I have quite a lot on my desktop. Maybe SpaceChem?
I'd go for something like MAME & get some arcade games happening, most of those only had the 4 primary directions and 1-2 fire buttons, you could probably manage that if you ap the keys to somewhere comfortable
you have feet don't you?

use them for keyboard and your good hand for mouse.

sure it will be difficult at first and you won't be able to use wsad configuration but arrows and space bar, ctrl will be possible.

unless you are sitting on laptop.

then

MMO2 is so much fun
Fallout 2 is considered by everyone (like me) to be the greatest game ever created by man and woman kind.
adventure games such as tlj. which is a classic
il sturmovik 1946 is also a good choice. you would crash with both hands anyway so with one hand you actually might have an edge.
Runespell Overture

Awesome RPG with turn based cardgame combat. You should try it!
Wow seriously? No one mentioned Heroes of Might and Magic 1-3? Pick it up play it awesomeness abounds! Plus yes it is TBS and all you need is one hand... :)
Its a completely different style of game then the ones said and finding copies may be difficult(though the new one release within the last year may also work-I haven't played it) but the "You Don't Know Jack" Games are very easy to play with just a finger. Although they may be a little boring alone after a while.