Most of my must have series are Nintendo; Zelda, Mario Kart, Smash, hence me buying a Wii U at launch.
But that's a boring answer.
So, game series that would make me buy any system:
Starfox Adventures maybe, really enjoyed that game, would love a sequel
A true Banjo sequel might do it (have to get over the Microsoft ick factor first)
A good F Zero
Can you tell most of my gaming memories were forged on the N64? haha
The PC games I once loved like Red Alert, CounterStrike and Baldurs Gate have kind of stopped being interesting to me. I think it's because console gaming is much better than PC for me now.