I'm starting to do a Bill here.
Caligula as someone has pointed out above, was the son of Germanicus, whom rumour hath it was killed by Augustus for some personal slight (or by Livia so that Tiberius would inherit the throne). He was well-educated, but knew full well that those in power around him had pretty much put paid to his family and trusted no one. He became bi-polar (well, that's the explanation I read somewhere; I'm no psychiatrist).
I'm not sure if there's any truth in the rumour that he murdered Tiberius on Capri (or had him murdered). Tiberius was actually not all that young and hadn't lived what you might call a healthy life since becoming emperor.
Caligula gradually completely lost touch with reality. I've read commentaries which suggest that Sejanus' murderous regime in Rome gradually eliminated all those around Caligula who might have kept him on an even keel.
I think that John Hurt's role as Caligula was something of a caricature. Still, he was a quite horrid little man, although probably not the worst of the Roman emperors from the point of view of the average vir in the via.
