Zelda series for sure, i've played and beaten all of them
Mario series also good, have also played and beaten most (have yet to do the E-reader ones)
Kirby series i didn't get into it much as a kid until the N64 game, then i loved it, and Kirby's Epic Yarn was seriously amazing, beat it in 28 hours (with multiplayer games with friends and family, no new levels, only prebeaten ones) i really hope they make a second Kirby's Epic Yarn
Super Smash Bros. series, also very good, the N64 one caught my attention, as a great fighting game, Melee, i kicked my bros ass 2 nights straight as Zelda! Brawl was EPIC i beat adventure mode (subspace emissary) on Intense mode as Zelda! it was freakin epic!
Mario Kart, very awesome series
finally, there is the Paper Mario series, absolute best series ever! the original Paper Mario was sick, seeing how awesome that was, i had to get the GC game, it was way more fun. then Super Paper Mario came out, i finished the game in 19h 59m and 12s!