So, I'll actually just answer the old question from, like what, the second post?
I'll answer this because I'm also going to post in the general gaming discussion what game series in general I like, and since there's a lot, I thought it'd be better to just mention the stuff that doesn't have it's own topic there.
First of: Super Mario
I generally like the 3D Platformers more than the 2D, and have played most of them. My favorite would be a tie between Super Mario World, Super Mario 64 and Super Mario Galaxy. The ones I didn't play were the first 3 by the way.
Now, next up are several child series to Mario:
A nice spinoff, with more emphasis on collecting treasure. And Wario Land 3 actually uses the same concept that games that are otherwise classified as Metroidvanias use.
Mario Kart and Mario Party
Theoretically you could also put all the other Mario Multiplayer games series here, but those two are the only ones I played. And since my mother is an actual gamer (tm), those games were always great for family evenings.
I'm actually not the biggest fan of these, but only because I myself am too bad at them. If I have a game I want to complete it 100%, for most of these games you have to perfect your play for the most part, since "mostly no damage" is part of this completion. But overall, good games.
Paper Mario and Mario & Luigi
The two RPG series. Great Humor, and, with exception of Sticker Star and arguably Paper Jam, at least a mediocre story. My favorite in terms of story is definitely Super Paper Mario, favorite in terms of gameplay is 1000 year door. For the record, I'm counting Super Mario RPG Legend of the Seven Stars here as well.
So let's continue with stuff that doesn't come from Mario.
The Legend of Zelda
I'm a big fan of Zelda. With the exception of 1, 2 and the CDi games I have played every single Zelda game. Favorite one 3D would be Majora's Mask, 2D would be A Link to the Past. By the way, I'm classifying Zelda games as RPGs.
And number 3 of Nintendo's big three:
Haven't played all of them yet, but enough to know that I like them. I like the concept of Metroidvanias, and the solitary exploring of the different places also gives nice atmosphere. Favorite one would be Super Metroid.
Nice, relaxing platformers that still give enough challenge if you want to 100% them.
Nice little RPG, which has music by Sakuraba. The collecting of the djinns was a nice completionist challenge, as well.
Continuing with RPGs:
Another big one. Was personally burned out after the fourth generation, so I passed on Black/White and Black 2/White 2, but X/Y got me back into it. I also liked the spinoff series Mystery Dungeon and Ranger. Overall, my mom is still the bigger Pokemon-Fan.
Now for a newer series:
I love this series and am actually considering to one day make a no death run of all three games.
Now, just to mention it:
I'll put more to this one in the Fire Emblem topic at a later point.
Also, by extension:
IntSys' sister series to FE, has some nice music, and for the first three, very silly plot. I mean, seriously, Andy, let's have another battle wasting soldiers' lives after this terrible war just because it's fun? (Also of course his infamous quote "What's an airport?" in the middle of the first game)
So let's hope I didn't forget a Nintendo series I like.
tl,dr: I like most of Nintendö's series.