I've not played the entire franchise, but these are the ones i liked more:
1. Mario Kart 64 (huge improvement over the first one, unforgettable if played in its time).
2. Mario Kart DS (Really good, with similarities with Crash Team Racing from PSOne, great variety of characters, vehicles and tracks, first one in the series to get online playing).
3. Mario Kart 8 Deluxe (The best overall, for obvious reasons, but it's a recent overexploited game with more than 8 years behind its back...).
The 4th should be Mario Kart Double Dash, which looks crisp and different from others because of the swapping mechanics but I've not really played it enough... Dolphin emulator or the GameCube emulation from Nintendo Online will help me to decide this in the future...
And the 5th position or even above, according to what most experts say and some gameplays I've seen, could be Mario Kart Wii, but I totally missed the entire Nintendo Wii system... So that's another one for the pending games list...