Part of the answer to this is dependent on what you classify as a "4-way" game.
In addition to the REAL 4-way games, you have off-shoots like Defender/Stargate that need alot of additional buttons.
The actual number varies with how you set it up in preferences.
There are also simultaneous multiplayer games that were "button-only" in the arcades, but would lend themselves to play with joysticks for the left-right functions.
This list would include Space Duel, Eliminator, and Armor Attack.