Definitely Mario Kart Double Dash. Mario Kart DS, Wii, and possibly Mario Kart 8 Deluxe are up there too. Super Circuit was good for the GBA. Mario Kart 64 is okay, its really the multiplayer mode that makes the game fun. Super Mario Kart was decent for being the first in the series. 7, while still fun and has good tracks, kinda disappointed me since it didn't have a Single Player VS mode. And 8 Wii U didn't have a good battle mode.
Mario Kart 8 for Wii U if mods are counted since I can play as Fawful. If not, Mario Kart DS for all the childhood nostalgia of playing it on any road trip.
(Actually Mario Kart Wii also has a Fawful mod, but I haven't used it since I haven't messed with MKW in quite a while so I'm saying MK8 due to having used the mod before and it obviously is higher quality)
Hard to pick a definite favorite so here are my thoughts on some of my favorites.
Mario Kart Double Dash was the first one I owned and was definitely a memorable one for me in terms of tracks, roster, and felt like overall it embodied the feeling of chaos that Mario Kart should have.
Mario Kart DS was very solid all around and feels like it's the foundation for the modern Mario Kart games.
Mario Kart Wii oh boy. This one really took the chaos to another level. I definitely appreciated the increase to 12 players. However, the balance in the game was pretty messed up. Bikes were pretty much outright better than karts and you had that awful item the ThunderCloud. Online was absolute chaos from Funkey Kongs all over the place, hackers, dropping from first place to last place in seconds. Honestly it was some of the most fun I ever had in an online game. Battle Mode online on Cookie Land was one of my most favorite gaming experiences. A shame the Wi-Fi connection was shut down. I know there's ways to mod the game to still play online but it's just not the same.
Mario Kart 7 like DS was a very solid entry and definitely one I put in a lot of hours playing the online. The flying and underwater gimmick feels pretty tacked on but it doesn't detract from the experience to me so it's fine (SATR Transformed did it better).
Mario Kart 8 (and Deluxe) I'd actually say is one of my lesser favorites. I played it a lot still but something about the pace of the game doesn't feel right to me. The courses on average feel shorter than in past games; Lakitu picking you up faster than in previous games makes falls feel less detrimental than in past games, and items as a whole feel less impactful as well. Overall the game feels faster but not in a good way to me, races feel more rushed. I also don't like the way items work in both the original game and deluxe.
Sad to say, while it was the first one I played I have no real love for Mario Kart 64. I feel like almost every later game outdoes it in most regards.
While difficult for me to decide, I have enjoyed playing Mario Kart 8, but I am retired from online play now.
Double Dash!! had something going with two characters in one kart, but the inclusion of special items meant that some characters were better picks than others. For one example, Donkey Kong and Diddy Kong both get the highly efficient Giant Banana, and it's an item that they can get in 1st place. Whereas, Peach and Daisy get the lackluster Heart, which can't even be acquired if you're leading a race.