Hi!
I happened to be poking around on roman-empire.net and saw something interesting about Caligula:
"[Immediately after Caligula's accession] it seemed that better days were in store. Much was to be hoped from a prince who was young, popular and generous - and who began his reign by liberating prisoners, recalling exiles, publicly burning incriminating documents, and showing great determination in the unaccustomed business of administration. But after a few months Caligula fell ill, and he rose from his sickness in effect a madman; bereft of all moral sense but not of that distorted but occasionally acute intelligence which accompanies some forms of mania. The new nightmare was more terrible that that which had passed with Tiberius. "
What would have happened had Caligula not fallen ill and therefore kept his sanity? Undoubtedly he would not be assassinated and would reign a long time. Furthermore, he would have likely had children, so he wouldn't start declaring people as his successors simply because they were attractive (there's one butterfly right there: Marcus Aurelius becomes a full-time philosopher and doesn't become emperor because his relative was handsome).