Gaius Julius Caesar Augustus Germanicus, nicknamed "Caligula" (Latin for little soldier's boot) by the troops in his father's army, ascended the throne upon the death of his great-uncle Tiberius in AD37. Initially he was hailed as a brilliant young ruler, a contrast to the aged Tiberius, and was by all accounts relatively stable and generous. Several months after assuming the Principate he either became very sick naturally or was poisoned by someone. In either case, he emerged from convalescence much more violent, impulsive, and all-out dangerous, if contemporary sources are to be believed. And herein lies the major source of questions about Caligula's sanity... quality of the sources available. The prevailing theory for a very long time has been that illness, poison, or paranoia stemming from these things rendered him irrational and insane. His extravagances and murders are the stuff of legend. Initial victims of exile and execution included close relatives (which lends some credence to the story of a poisoning that didn't quite do the trick). He began executing people without trial, mostly to seize their estates. Later "follies" include extravagant construction projects at a time of severe economic depression and famine, accusations of incest, failed military campaigns, an attempt at attacking the sea using the Roman army, and the appointment of his horse to the senate... rather any of this is true, or to what degree, is all fairly open for debate given the sources (See below). Even so, he did enact some reforms that could be seen as positive, such as reinstating relatively democratic elections.

So, outside looking in he appears to have gone insane, or at least become severely megalomaniac. We are hampered in an exact diagnosis because many of the sources available for his reign (Josephus (a small child when Caligula was emperor), Suetonius (writing ~80 years after his reign) and Cassius Dio (writing nearly 200 years after his reign) are prominent ones) post-date his time on the throne and may have been written with ulterior motive/scandal-mongering/etc. in mind. On the other hand, these Roman historians had access to now-lost contemporary sources that we do not, so one could argue they had a better perspective on the "true" Caligula. Suetonius stated he was not just insane but epileptic. Josephus states that he went insane due to conceit and ego. Philo of Alexandria, a contemporary and sent as ambassador to Caligula on behalf of the Jews of Alexandria to help resolve a dispute with the local Greeks, thought him to be crazy and observed that he went off his rocker after becoming sick shortly after he assumed the throne. Of the contemporary sources Seneca is most prominent as a well-known member of "high society" and a philosopher and statesman. Seneca clearly states that Caligula was insane, and that power made him so. In fact, he uses what happened to Caligula as a warning/parable for how power corrupts. Caligula nearly had him killed, though (Nero, another emperor not remembered for his gentle and sane manner, eventually forced him to commit suicide, succeeding where C. failed), so accusations of bias on Mr. S's part are possibly not unfounded. That aside, well, it does appear that something was a little off. We have a confluence of surviving ancient sources, contemporary and later, that all agree he had issues. How much they can be trusted is another question, but so far as I know there are zero ancient sources that label him healthy, benevolent and sane.

So to sum up... well, there is simply a lack of hard facts, but the weight of the writing from classical times favors the idea of a disturbed person. Was he insane, a brutal dictator, or has he been the victim of continuing bad press? Open question. I guess the important question is, how did he fit in from a contemporary point of view... that is to say, was he more megalomaniac/extravagant/brutal than your typical dictator throughout history? Tough to say, but he has been popularly remembered as being so. He was assassinated, but so too were the majority of Roman Emperors so that proves little about his sanity. Sources: the historians listed above, primarily, combined with Michael Grant's historical/biographical writings on Rome.

According to Suetonius and Philo of Alexandria, he became insane after falling seriously ill in October of 39. The historian William Dunstan believes that he may have been poisoned. Did this drive him insane? We don't know for sure, due to biased sources.

However, we do not that before this poisoning, he abolished treason trials, increased military salaries, and threw spectacular gladiatorial displays for the common people. These moves were financially irresponsible, but they appear genuinely well-intentioned.

The year after his poisoning, he had his adopted son Tiberius Gemellus killed, he exiled his sisters, and he declared that he was the grandchild of incest between the Emperor Augustus and his sister.

The next year, according to Suetonius and Seneca, he engineered a famine (by seizing public carriages and grain boats) while Rome was already in a financial crisis. He proceeded to renew the treason trials he had abolished.

I'm inclined to believe that a period of severe illness resulted in him being mentally ill.

That being said, due to the biased nature of our sources, we can't be sure. Its possible that he was a naive young ruler, who discovered that his generosity had cost him his fortune, and that someone had poisoned and nearly murdered him. These experiences could've hardened him, and what was portrayed as insanity was in fact the cutthroat political maneuvering that was the norm in Rome.

Sources: Seneca, Suetonius, Philo of Alexandria