I would say Pokemon obviously. Animal Crossing is another one.
I only really enjoy Mario games when they're RPGs or if it's Luigi's Mansion. (or is that a Luigi game?) Mario side scrollers are beyond boring and games like Mario Sunshine and Mario Galaxy keep me content but not really excited.
I have a mixed relationship with Zelda, I do like the games but I normally don't finish/get bored of the 3d adventures. I never finished Skyward Sword because that mini game where you had to run around in spirit world from the ghosts was too frustrating + boring. Bad combination.
I love Zelda's 2d adventures like a Link to the Past and the Oracle games, I'm looking forward to playing Oracle of Ages when it comes to virtual console because I only played Oracle of Seasons.
I've never actually played a Metroid game, well that's a lie I played the Metroid Fusion game we got in the free virtual console games. Really I wasn't that impressed...I don't think Metroid is for me although I'm willing to try out the 3d ones at some point.
Also it's not a series yet but if it's true that a new Xenoblade Chronicles game is coming to the Wii U I would include that series.
Also I really like the Earthbound series, Nintendo took their eye off the ball when they didn't localize that game.
I tend to shy away from the popular Nintendo experiences these days (Mario side scroller/Zelda adventures) I personally don't feel that's when Nintendo are at their best.