Rules! I won't pick any games that don't have at least two entries, or at least have a second one on the horizon.
Wii-Super Smash Bros.(unanimously)
360-Dead or Alive(I would have picked Bioshock, but it's not a series yet)
PS3-Ratchet & Clank(There are plenty of games I like more, but most have never appeared on PS3 yet. It was between this and Resistance)
DS-Advance Wars(Unanimously-Plus best series in the world)
PSP-Pursuit Force(That's the best I could think of. Every good game series appears elsewhere. GTA, MGS, Disgaea, Syphon Filter, Jak & Daxter, Ratchet & Clank, GOW, WipEout)