Mario Kart Wii - The course designs, music, extras, and the online play (when it was active) were all very good. In my opinion, it's the best entry in the series.
Wii Sports Resort - Just the whole vibe of the game itself was enough to have me come back to it, even if I wasn't a fan of all the games featured. The seaplane flyaround and collecting the "i" points on Wuhu Island was also cool. I even named my New Horizons island after it (though at the time I didn't know that it was spelt "Wuhu", but honestly, I think my spelling is better).
Mario Party 8 - In my opinion, the last good Mario Party game before Hudson shut down and the series went down the drain for a while.
Animal Crossing City Folk - Pretty self-explanatory. It's the game that got me into the series in the first place, though it didn't take until late in New Leaf's popularity for me to become a big fan.
MySims Kingdom & Agents - Say what you want about this series; I thoroughly enjoyed these games. I wish they were longer, however. I recall completing Kingdom in a day.
Wheel of Fortune - A game I started liking after playing it with my family. This version is great in that I've played it many times and rarely encountered duplicate puzzles. A very faithful adaptation to how the show was played at the time, and I think it's better than the Switch version. Oh, and you get actual voiceovers from Pat Sajak, Vana White and Charlie O'Donnell!
WarioWare: Smooth Moves - It's a very fun (and funny) game. Playing it with a group of friends is even better!
I've still yet to try some of the other popular titles (Super Mario Galaxy and its sequel are among them), but many of the games I listed above played a big role in my childhood growing up.
Hm, that's a tough one, as I haven't really branched out to try other games. There was probably one game I rented at my (now long gone) video store based off the cover art alone, but I can't remember what it was. It was either a Wii or PS2 game that had some form of driving mechanic, but it wasn't the main thing of the game.
In terms of what I do own, it's hands-down Myth Makers: Kart Racing GP on the Wii. I don't even remember how I got that game, but it was likely a gift from a family member one Christmas. If you're aware of who Data Design Interactive were, they made a ton of bad games for that system. The motion controls alone are enough to make me want to throw my Wiimote out the window.