Tough question. I like a lot of Nintendo series because of Smash, and it's somewhat influenced by my character choices. I guess I'll just make a list, since picking just one would be painful:
My Favorite Series (No particular order):
-Mega Man (Played all of them.)
-Punch Out!! (Played the NES one, plan on getting the Wii game.)
-Wario Land (WarioWare is cool too but I like the platformers a little more. Played them all.)
-Mario/Yoshi (Played pretty much all of them)
-Kirby (Played every notable/main game except Mass Attack)
-Pokemon (Not very competitively, played every gen)
-Fire Emblem (Only played Gaiden, liked it, and am getting Awakening.)
-Earthbound (Beat Mother 2, 75% done with Mother 3, but I haven't played it in a year. Mother 1 is painfully slow though.)
-F-Zero (Only played X, love it)
-Animal Crossing (Started on Wild World, got every game since.)
-Game and Watch (I love G&W Gallery 4.)
-Zelda (Haven't played it a lot but what I have played is great. The NES games are fun and challenging and Wind Waker HD is amazing.)
-NES (I have played Ice Climber and Gyromite. I like them a lot, but not as much as other launch titles.)
I don't know/like these enough:
-Donkey Kong Country (Didn't like the first game that much, but I love DK64.)
-Kid Icarus (Hate the NES game, haven't played Uprising or GB)
-Metal Gear (Own the NES game and that's it)
-Metroid (Again, only played the NES game really. Not my kind of game.)
-Wii Fit (Haven't tried. Probably won't.)
-Sonic (Like the Genesis games, and hate most of the 3D ones I've tried. I don't really like that series much at all for it's boring irritating characters. Sorry Sonic fans, it's just my opinion. I think they overcomplicated a fairly simple and straightforward series.)
-Star Fox (Very unfamiliar with the series. Played SNES and 64 but it wasn't very exciting to me. I prefer sidescrolling shooters like Gradius.)
-Pikmin (I rented it once for Wii. I liked it but it got difficult rather fast.)