No 2 player 4-way diagonal games that I am aware of.
Karate Champ can actually need as many as 4 4-ways.
Other 2-player simultaneous 4-way games (or dual 4-way).
Xybots (software supports 8-ways, and it actually plays better with them, but the cabinet itself shipped with 4-ways).
Hyper Pac-Man
Assault
One (or both) of the Namco Classic collection games needs dual 4-ways for 2 player "arrangement" mode, not sure of the current status of these in Mame though.
One of the hacked versions of Ms. Pac-Man lets player 2 control a ghost.
Bloxeed
Many puzzle games play much better with a 4-way, and most of these are 2-player (Magical Drop, MIExchanger, etc).
There are others, yes there was a recent thread about this, but I can't remember the name.