Objectively it would be Mario... This is an established-by-numbers facts.
It has made the most money, sold the most copies, and the latest Mario Galaxy is to my knowledge the first game ever (I might be wrong though) to sell 500 000 copies in the first week of it's release, proving that Mario is still one of the most important video game icons ever.
My personal favorites would be the Kirby, Megaman and of course Super Smash Brothers series though.
I simply enjoy Kirby so much because of it's simplicity and it's fantasy elements. Makes a great escape from every day life, where things are reality instead of fantasy and where stuff tends to be more complicated rather than simplistic.
I enjoy the feeling "childish amazement" that Kirby gives me.
(Yes I'm a death metal/extreme rock fan on one side, and a kirby fanboy on the other, it's perfectly possible
)
I also have a thing for taking on the role of characters who can use different powers. Just because it adds further to the imagination.
And, come on, he get's to fight a hammer-weilding penguin, a wind-blowing tree and a gang of treasure-hunting mice. It's too cool!
Megaman X I simply enjoy because I grew up on Megaman games. Megaman X is just like the Megaman games but with a deeper storyline to it and I like it like that.
Other franchises I greatly enjoy are Final Fantasy, Metroid, Klonoa (earlier games), Crash Bandicoot (earlier), Spyro (earlier), Pokemon, Kingdom Hearts and some fighters (Tekken, Street Fighter, Mortal Kombat) and some horror games (Resident Evil, Silent Hill, Eternal Dark)
Final Fantasy once again for the deep storylines. Metroid because I like the combination of science-fiction and adventuring/item collecting. Klonoa, Kingdom Hearts and Spyro for pretty much same reason as Kirby.
