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.