Updated: Mar 14, 2021
Hexcite: The Shapes of Victory (Landwarf/Ubisoft, 1998)
I can only assume this is a port of a forgotten board game. You and your opponent play tetronimoes to the board, but I could not figure out what determined whether I was able to play a piece on a space or not.
Hiryuu no Ken Retsuden GB (Culture Brain, 2000)
This is a long-running fight game series that I believe has some respected entries, but this particular version is a disaster. The A button seemingly only works at all half the time, and even then it's on a ridiculous delay. You can sort of get away with it since your opponent plays like they're suffering from the same problem, but I wouldn't call that fun.
Hissatsu Pachinko Boy: CR Monster House (Sunsoft, 2000)
I don't particularly understand why anyone wants to play pachinko, much less why they'd want to do it on GBC. This one would at least work as a nice screen saver, because you can press select to add 250 credits and then just leave it firing balls on the same arc until whatever huge number you've set it to runs out. It's extra weird that they let you set the power that precisely since if you actually cared about this you could do what I said and leave it firing at the best spot on the board every time.
Hole in One Golf (Natsume/Epoch, 1999)
One of the more unique golf setups I've seen. It's a top down view of the entire hole until you commit to a shot, at which point it zooms in to show the screenshot above. Your power meter works more or less the same as always, but you determine where you hit the ball by stopping the crosshairs as they zigzag up and down it. That part is really hard to control, probably explaining why this mechanic never took off.
Hollywood Pinball (Tarantula Studios/Take-Two Interactive, 1999)
This one only released in Europe and Japan despite being named for a place in the US, oddly. Pinball isn't much more enjoyable to me than pachinko, so I didn't play much of this. The button setup isn't anywhere near as crazy as the last pinball game that came up, there are some fun board themes, and the music is pretty good. Probably a good time for someone who likes pinball.
Honkaku Hanafuda GB (Altron, 2000)
I still don't know how to play Hanafuda, but this version of it at least tells you which cards you can play on your turn and has some fancy animations for dealing and shuffling cards.
Honkaku Shogi: Shogi Ou (Warashi, 1998)
It's shogi without any particularly remarkable features. You could play two player on the same device, I guess.
Honkaku Taisen Shogi Ayumu (Culture Brain, 2000)
Pretty much the same as the other game except that the graphics look much worse. You'd think it'd be the other way around since this one came out two years later.
Honkaku Yonin Uchi Mahjong: Mahjong Ou (Warashi, 1999)
Ricci mahjon, but everything is really hard to see. This is definitely a terrible way to learn the game, and it seems like a terrible way to play it even if you're already deeply familiar. It did at least have a character select for the other three players, although you're not going to get a ton of variety from that when there are only six total characters.
Hot Wheels: Stunt Track Driver (Lucky Chicken Games/Mattel Interactive, 2000)
A much younger me had a PC disk of this game that didn't work. That was one of history's great tragedies to that me. I don't think I ever got this version, which is just as well considering it kind of sucks. You hold down A to go and press directions on the dpad to do a flip or a roll in the air, which will make you go faster when you land. The tracks are straight, so that's all you ever need to do. On the bright side, I guess it's simple enough for even extremely young kids to play? It's not good, though.