Has anyone gotten more mileage from mumbling than Benicio Del Toro? Sure, Marlon Brando and James Dean were called mumblers back in The Day (i.e. the early 50s), but they were at the forefront as method acting graduated to the big screen in a big way. Brando quickly expanded beyond the mumbling reputation, and, even though he only had three pictures as a star to prove it, James Dean had a huge range of emotions and speech patterns.
More recently, the so-called mumblecore movement may have gotten a slight bit of traction because of the term, but it wasn't truly reflective of how most of the characters in the (mostly) unrelated films actually talked. "Talking so softly as to be indistinct" or "not knowing how to enunciate their words in a natural way because they weren't really professional actors" might be a more accurate designation.
No, good old Benicio Del Toro is the current standard bearer for mumbling, and we can thank the cinematic gods -- and Del Toro's own instincts -- for that. Because his manner of talking in a sing-song, irregular-rhythmed netherworld between English, Spanish, and "Huh?" has made us pay more attention to the character speaking the words. Which is why, I think, so many people will see The Wolfman and ignore the critical pans that it's receiving. (Our own John Gholson says it "truly is a modern spin on a classic, in almost all of the worst ways.")