F1 Racing Championship (Ubisoft, 2000)
Apparently the PS2 version of this was notable for having GPS-modeled all the tracks and using a 360 degree camera to capture even small track details, but obviously none of that comes through on GBC.
F-1 World Grand Prix (Video System, 1999)
A much better racing game that has an impressive sense of speed thanks to a really zoomed in camera. It had (very simple) damage modeling and weather, which hasn't been in any other GBC game so far.
F1 World Grand Prix II (ITL/Konami, 2000)
The only F1 GBC game to release in the US, and the only one with music on track. Other than the pretty good music and better UI, it's exactly the same game as the original. I'm not sure why one says "F-1" and the other "F1."
F-18 Thunder Strike (Morning Star Multimedia/Majesco, 2000)
For the latest in the "can we/should we" dichotomy, we have a game that answers "yes, you can make a first person flight sim on GBC." But should you if everything outside the cockpit has to look like it was made in MS Paint in about 10 seconds? Probably not. I have no idea how you're supposed to find anything without a real radar, or why this plane is only equipped with a gun.
Fairy Kitty no Kaiun Jiten: Yousei no Kuni no Uranai Shugyou (TOSE/Imagineer, 1998)
The title translates to something roughly like "Fairy Kitty's Lucky Time: Fairy Country Divination Training", which would explain why all the minigames seem to be purely luck-based. In the above minigame, you need to flip over cards without seeing the symbol on the left, but it's placed randomly each time. Your total score persists through failed runs, so you probably progress if it gets high enough. There's also a Frogger-like game where the spaces you step on randomly sink into the river and end the game. It's really not fun.
Ferret Monogatari: Watashi no Okini Iri (Culture Brain, 2000)
"Ferry Story: My Favorite Pet" is another tamagotchi style pet raising sim. But, as you may have gathered from the screenshot above, it also has a minigame in which your ferret puts on sunglasses and dances. It's an awful rhythm game that's about 10 times slower than it should be, but points for the visual.
FIFA 2000 (Tiertex/THQ)
I'm not sure why they bothered with the FIFA license if the game was just going to be indistinct national teams playing each other in a generic stadium with no player names. It's also presented in an isometric view that makes it unnecessarily difficult to control and see what's happening. It's not the worst GBC soccer game because that's a really high bar, but it's far from the best.
The Fish Files (7th Sense/Microids, 2001)
A Lucas Arts-style adventure game that seems to have been received pretty well at the time. This screenshot is in Italian because I couldn't get the text to advance the first time I tried it in English, and then I accidentally mashed through the wrong language. I never got to gameplay because the text started barely advancing again and the game crashed right after this was taken. I couldn't be bothered to sit through the opening for a third time in a row.
Fix & Foxxi - Episode 1: Lupo (Similis/Ravensburger Interactive Media, 2000)
A character platformer that seemed decent enough. It has a kind of Getting Over it With Bennet Fody element where the whole stage progresses vertically in a back-and-forth pattern, so if you miss a jump you can easily fall all the way back down to the start of the level. It was one of a handful of games Ravensburger published before deciding to stick to board games and puzzles.
The Flintstones: Burgertime in Bedrock (Conspiracy Entertainment/Classified Games, 2001)
I don't know what I expected, but it was somehow not Burgertime with a Flintstones reskin. That's really all this is.