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Curly is bald because Moe yanked out all his hair.
We see Moe yank wads of Larry's hair out from time to time, but because he doesn't abuse Larry as much, Larry is still only semi-bald. This is also supported by the occasions where Moe tries to pull Curly's hair, as if it were a reflex, but finds nothing to grab ahold of. And his nickname "Curly" may have been given to him because he used to have curly hair. 
The Three Stooges are Toons in disguise.
This goes with a WMG on the Who Framed Roger Rabbit page. They're wearing human-like costumes, kind of like Judge Doom was.
The Three Stooges are Toons trapped in the real world.
That explains why they can't be seriously injured by stuff that would give them a trip to the hospital (I.E. Getting hit in the head with a bottle) Or getting killed with stuff that would normally render them dead. (I.E. Falling from a 20 story hotel)
The insane man from the short "Men in Black" is Professor Theodore von Scharzenhoffen from the Laurel and Hardy short "The Music Box"
They're both played by the same actor, Billy Gilbert. "Men in Black" takes place shortly after Professor Schwarzenhoffen has been driven insane by the antics of Laurel and Hardy.
The stooges have been reincarnated all through history.
Hence we get episodes where they're cavemen, or in ancient Rome, or in the American Civil War.
Alternatively, the Stooges are Immortals a la Highlander
Duncan MacLeod probably knew them back in the day.
Curly is a Time Lord.
Every wonder why The Stooges are in different time eras? This might be how they are able to be in the Roman era, then suddenly to Caveman times. Also, Curly is able to be reincarnated as Shemp, Joe, and Curly Joe. 
Shemp will appear in The Movie as a cameo.
The Three Stooges was always Moe, Larry, Curly, and Shemp.