How can we forget about UGH!

If you will bye a gamepad (with two analog sticks), try this (My favorite split/shared screen games): Magicka, Kane&Lynch-Deadman, Resident Evil 5-6, Trine 1-2, WWE RAW, Castle Crushers, TMNT series, Obscure 1-2 (in second part don't skip titles at the end), LEGO, Terminater salvation, Portal 2 and left4dead 1-2. Also Portal 2 and L2D 1-2 can be played on two screens and one PC simultaneously.

Little Fighter 2.

Turn based stuff like Civ V and Frozen Synapse have hotseat.

The LEGO series :)

Wow, I haven't shared a keyboard in so long that I'd forgotten it as an co-op option. The last game I played via keyboard co-op was probably something from the You Don't Know Jack series.

Thanks badaboom for inspiring this helpful list. Bookmarked for future reference.

Obscure

Any Lego game has local co-op.

Any Worms game

Colin McRea Rally 4 had a local coop up to 4 players.

Micro Machines!

Oh, wrong century, my fault ^^

atomic bomberman
mortal kombat
worms
SRS
tbs games (panzer generals, homm3, disciples ...)
lotr3 (I`m not sure about this one tho)
arcade console games emulated on pc

you should probably buy a cheap keyboard / gamepad

Audiosurf

Sumotori, one of the funniest games ever created.

My wife and I do this all the time. But I use a mouse and keyboard while she uses the controller. I tried doing local co-op on some old SNES emulators back in high school, but it was just too cramped. Though I suppose if you have one of those ergonomic keyboards with the separated sides it wouldn't be that much of a train wreck.

Anyway, I'm throwing my vote in with any Turn Based Strategy game. The Civilization series is amazing.

CO-OP QWOP super funny to play with someone get some hilarious scenarios

Stepmania

How about that Dubai Scandal game about the camels?

Audiosurf for sure! If you play the double vision mode one of you gets the mouse and the other the keyboard.

In the same rhythm based genre you can also download StepMania. Quite fun to DDR it up on a keyboard with a friend.

Dungeon Defenders