Theme Hospital and Dungeon Keeper (1 and 2) can easily be played without keyboard support and are both great games.
Monkey Island, Escape from Monkey Island, Curse of Monkey Island are all good-great games. The only time you need the keyboard is to open the menu and save.
Broken Sword is a great game, only mouse needed. The ending is weak but not disapointing. Its sequel is fine but it is very mediocre.
The Beast Within is a good point and click adventure... however the last few puzzles are all rather poor. Could be worse, Gabriel Knight (the first game) was made out of really REALLY tough puzzles.
The Sims 1, 2, and 3 are all keyboard free (you can use it but it isn't required) for all but inputting names on your sim and an optional Bio.
Phantasmagoria is in my oppinion an underrated point and click horror game that doesn't attempt to outright scare you off the bat and a GREAT musical score for a horror. No Keyboard except for saves as well.
Majesty and Majesty 2: While the first is a classic and the second... well it is alright. They are both good strategy games that do not require the keyboard. While you could use it, I certainly never found the need to.
I find suggesting Freedom Force (either 1 or 2) rather iffy. The only thing you need the keyboard for is pausing, which you will need to do quite often especially on harder difficulty settings.
Ghost Master: A very fun puzzle game that can eat up quite a bit of your time. The game is unfinished but honestly it is fine on its own. If you have no sense of being a completionist then it probably isn't for you, afterall collecting the ghosts themselves is half the challenge.
Rollercoaster Tycoon: Extremely fun and simple at its heart. Check it out!
Zoo Tycoon: Fun, but while Rollercoaster is simple, Zoo Tycoon can be annoyingly difficult. You often won't know why you are or are not making money.
I probably have many more to suggest. Until next time I guess