Honestly, I've always loved the compelling stories and gameplay that the Zelda series has brought, and the fact that every single new Zelda game has changed the way the series is played significantly. There's always some new gameplay element added that makes it feel like an entirely different game than the last one, without detracting from the fact that it's the same 26-year old series.
Mario and Pokemon are also great franchises, however Mario's games are really non-canonical with each other and the story is typically an excuse for a new gameplay element. Pokemon is also a great series, however the story is always "meh", but they're still wildly fun games. I just recently threw a GBA emulator onto my phone and have started replaying Pokemon the other day (though it's a lot more fun on DS, since I can easily import the Pokemon from my old GBA carts and play online and stuff).