I'll open up the topic with: What do you are your favourite Nintendo-owned game series'? They can be anything from Mario to something obscure like Jam with the Band, as long as it's Nintendo owned!
For me, I'll name four.
Kirby. I freaking love Kirby games. He's starred in a lot of different titles, some better than others, but I continue to insist that Kirby knows how to be a fun game more than any Mario platformers do. The concept is so simple, but the gameplay usually goes quite deep with all the hidden collectables you can find to reach 100% completion. And often, the multiplayer is amazing. Kirby's also one of those franchises that isn't afraid to dabble in many spinoffs, and the results are often very entraining, sometimes more entertaining than the main entries themselves! cough Kirby Air Ride & Canvas Curse cough
Fire Emblem. It's a shame it took this series so long to reach international waters, because it's amazing fun! The permadeath system creates a very unique dynamic to strategy, where every move made on the battlefield matters, and you feel genuine attachment to the narratives of your little pieces on the chessboard, and it pains you whenever you see them in trouble. My housemates always give me weird looks because I'm always shouting or gasping with relief whenever I play awakening, because there's so much suspense with every turn! It's the most exciting of all when a unit faces almost certain death, and you have to pull off some crazy tactics involving your entire army just to keep them alive.
MOTHER/Earthbound. Holy shit release MOTHER 3 in English already Nintendo! This series is very near and dear to my heart. Not just for the quirky and hilarious dialogue ever-present in the stories, but also how the stories deal with some very strong and mature themes. MOTHER 3 in particular deals with themes like grieving over the loss of a loved one during the already-turbulent time of puberty, the influence of technological advancement on mankind, and the ultimate fate of the world. These games are deep shit, and much like Key games, will probably bring you to tears at some point. It's not all fun and games.
Metroid. A very popular one, but a very deserving one. There haven't been many Metroid games, but nearly every one has been amazing. Even OTHER M, the one everyone complains about, is something I enjoyed a lot despite it's flaws. It felt like a more natural transition to 3D than the Prime series did, like the missing link between Super and Prime. That said, Super and the Prime series still remain very near and dear to me. Especially Metroid Prime 2! That game was amazing. The feeling of exploring an alien planet and all the action of the combat is really exciting, and it's always a joy to reach 100% completion in those games.
Let's hear some of your favourites!