Wow, we have a bot of misinformation here.
I did two buttons on my dedicated 4-way cabinet. There isn't really anything worth playing that has more than that.
Every controls list I have ever seen floating around is riddled with errors.
First lets look at the "3 button games" listed above.
Iron Horse (dairesya, Far West) is an 8-way game, just played it, and it definitely has diagonal movements (and it sucks too).
Karian Cross is a puzzle game, and like almost all puzzle games, it plays equally well with 4-way or 8-way. You would want to use 8-way anyway, just so you can play 2 player.
The Logic Pro games are in Japanese, and it is a Mahjong Puzzle/Quiz type deal. Unplayable unless you can read japanese, and it probably works fine with an 8-way, not like those Mahjong games are based on precise movements.
Punchout is worthless in Mame due to the stupid twin display thing.
Reikaids is a SF2 style fighter (and probably dated wrong too, as those graphics look a bit above what some no name company could have done in 1988), and have you EVER seen a 4-way fighter?
Tutankham is not a 4-way game, it uses an 8-way top fire along with a 2-way.
Zero Zone is a porno Columns clone, and like all puzzle games it plays just fine with an 8-way.
Now lets look at the "4 Button games"
Chinese Hero has 4 inputs listed in Mame, but try playing it, the 4th button does not do anything that I can see. I am guessing the 4th button is left over in the driver from some other game that uses the same hardware. It is however a true 4-way game, but it is kind of like Legend of Zelda or Bomberman in the movement area, and it plays just fine with an 8-way.
40 Love also appears to just be a 3 button game (another Taito one, like Chinese Hero). It is also a true 4-way game, but it is also a total mess, and there are much better Tennis games in Mame. Tennis is simply not a 4-way type game, and I have no idea what Taito was thinking with this one.
Mouse Trap is the ONLY reason to have more than 2 buttons with a 4-way stick. It has 4 buttons, but it also isn't THAT great of a game. Unless you really like it, then it can be skipped, there are a lot of other similar games with less buttons.
Super Punchout, like Punchout is a mess because of the dual display issue.