Javier Bardem as Anton Chigurh.
Reagan when she was possessed.
I can’t believe you beat me to it.
I suspect that many of you are not familiar with Dr.Phibes, but I would say that he’s streets ahead of any other movie maniac.
For second place I offer Dr.Strangelove.
Mitch Leary.
Rocky Horror’s Frank N. Furter/ Introduced Tim Curry, and he can sing and dance!
Cody Jarrett.
Dr. Evil.
Anton Phibes? The Abominable Doctor Phibes?
Never heard of 'im! 
And I’ll throw in Edward Lionheart! (Theatre of Blood)
Looking through the responses before posting my own choice, I have to say this is the best so far for me.
I also enjoyed Roy Batty (Rutger Hauer) in Blade Runner although his “madness” was acquired. 
De Niro: Max Cady in Cape Fear
“…leaning, leaning!
Safe and secure from all alarms!
Leaning, leaning!
Leaning on the everlasting arms…”
Would you like me to tell you the little story of Right Hand-Left Hand - the story of good and evil?
Hauer was a “good” madman in The Hitcher, too.
^Could a mod please delete this post? There is no Keyser Soze.
I think I love Rhombus.
Hjalmar Poelzig.
Bonus points if you know who this is without looking.
I’m a big fan of John Goodman as Madman Mundt in Barton Fink. He’s pretty well endowed physically, AND he’ll show you the life of the mind.
I will give votes to Alan Rickman at any opportunity, but I feel compelled to point out here that he was not a madman, but a common thief. I mean, an *exceptional *thief!
Best movie madman? Jack Torrance of the Shining, or Gene Wilder’s Willy Wonka.
I’d back Powell in a crazies-cage match with most of these others.
OK, you got me. Who is this?