Fair enough, we might not have similar tastes but here are some of my favourites. Sounds like you're the most unsure about the Nintendo games so in the interest of my reply not taking up the page I'll stick to their stuff, though I'm not a fan of the 3DS so can't really suggest 3DS games.
Wii
No More Heroes 1 & 2 - My personal favourite Suda51 game/s, these just feel great to play and the bosses are awesome. Second game in particular is brilliant. There is a PS3 PS Move port of the first game, but it's inferior imo.
Madworld - Platinum game, use the environment to kill enemies in as brutal ways as you possibly can while a duo of commentators provide commentary for your actions. It's just cruel gory fun.
Trauma Centre: Second Opinion - Never thought I'd be drawn in to the story and characters of a waggle control surgery simulator game. The gameplay is pretty good too though, feels really tense.
Beat the Beat: Rhythm Paradise / Rhythm Heaven Fever - Really fun rhythm game, I can play this for hours. If you're from America though it might not be as good, in the EU version you can enable the Japanese versions of the songs. I ain't no weeb but the English versions sound sort of artificial and unnatural.
Wii U
Splatoon - Goes without saying, you probably already have it if you have a Wii U but it's insanely fun. The online is still pretty much alive despite 2 being out but since the Splatfests have ended and the game's stagnating now I'd say you're probably better off moving to 2 if you have a Switch. 1 and 2 feel subtly different though so it's still worth playing. It's a shame to have missed it in its prime.
DS
9 Hours, 9 Persons, 9 Doors - First game in the Zero Escape series which has a small but almost dangerously obsessed cult fanbase. And I'm in it, these games are amazing. If you're into narrative-driven games you owe it to yourself to play them. Might not technically call it an exclusive since it's now been ported to PS4 and Vita, but the port version is modified to fit the new consoles in a way that I can't explain without spoilers but is pretty disappointing. This game can only work on the DS or 3DS.
Pokémon Mystery Dungeon: Blue Rescue Team - This game is honestly surprisingly good. It's a roguelike dungeon crawler which you may or may not be interested in yourself, but getting and evolving Pokemon in this is somehow even more engaging than in the main series. And there's just something generally about the game that draws you in. I can't recommend the other Mystery Dungeon games personally though, they feel unnecessary and stripped down.
Radiant Historia - Underrated JRPG, I haven't finished it but it's a traditional JRPG where the story takes place simultaneously over different parallel timelines, pretty interesting concept.
Castlevania Order of Ecclesia & Portrait of Ruin - Castlevania is great. Only reason I haven't included Dawn of Sorrow though is because I haven't played it, I'd assume that's good too.
Phoenix Wright: Ace Attorney series - Another one I probably don't need to explain, they're good. Can be stressful as balls if you don't know the answers though.
