This is very hard because they have done so many great games. Mario, Zelda and Metroid are perhaps the greatest series not only on Nintendo´s platforms but by any standard. I also love Mario Kart (which I definately consider a series of it´s own).
My favorite game of all time, SUPER METROID!
Favorite series (by a small margin) ZELDA
Best games in respective series for me:
Mario: SUPER MARIO GALAXY WII
Zelda: ZELDA- A LINK TO THE PAST SNES
Metroid: SUPER METROID SNES
Mario Kart: MARIO KART WII