I think it's kinda hard to claim any cartoon character that's come out very recently to be among the greats unless it's truly, truly groundbreaking or unique; but with that being said, it's not gonna stop me from touting the recent ones.
Homer Jay Simpson is definitely up there, Stewie Griffin of Family Guy is close, but I'd also have to say Bugs Bunny, Huckleberry Hound, Yogi Bear, Scrooge McDuck, Chilly Willy the Penguin, and Mickey Mouse.
While we're at it, why not add Stitch (Experiment 626) and Eric Cartman to the pile, too?
Does Boba Fett from the SW Holiday Special count? hehe