This thread is a goldmine. I'm also weirdly proud that I recognize a bunch of them.
Ironically, Nintendo would end up using this feature, not on the Wii... but on the Wii U!
Splatoon 1 has a 2 player local multiplayer mode that is only playable if you play by connecting both a Wii Remote and a Classic Controller and taping them together. I shit you not!
Actually, there is a post on the
Live from Squid Research Lab blog post explaining this "discovery"! I didn't know that the slots behind the Classic Controller were actually meant for an add-on like that though. It could probably made by 3D printing it nowadays. It surprises me that they already added the slots way before the release of the Wii Motion Plus accessory. I don't really see an use to slapping a Wii Remote to a Classic Controller since it does not have a gyroscope. Maybe they already knew they would release the Wii Motion Plus. Which makes it even more surprising to me that they did not add a gyroscope to the Classic Controller Pro or the Wii U Pro Controller.
Anyway, talking about the Classic Controller! The original Classic Controller has GameCube-like analog shoulder buttons. These were removed on the Classic Controller Pro. I remember there was a list of games that supported this, but I can't seem to find it. There are a bunch of Wii titles that
supported GameCube controls as well, which was awesome. And special shout-out to Super Smash Bros. for Wii U. It supported the Wii U GamePad, Wii Remote, Wii Remote and Nunchuk, Classic Controller, Classic Controller Pro, Wii U Pro Controller, GameCube controller, and the Nintendo 3DS systems as controllers.
I'm sure there are a bunch more bizarre features that I can think of, but I don't have a lot of time. One of my favorite weird consoles is the Nintendo DSi. Even though it was not possible to play GBA games on it anymore - and with that, we lost
Nintendo DS with GBA connectivity - it still has some weird quirks that make it unique such as it's own music player, camera, gallery (which allows you to share a picture on social media) and of course DSiWare. One bizarre feature is the addition of animating game icons. Pokémon Black, White, Black 2 and White 2 support it: The game icon is animated when viewed on the Nintendo DSi or 3DS home screen—the Poké Ball inside the icon wiggles. There's only an incomplete list that I found
over here.