The one that immediately comes to my mind is the Great Fire in Rome in 64, during the reign of Nero (I'm writing my dissertation on the guy). Although there were a lot of other big fires in Rome, which was a particularly flammable city (lots of tiny streets with wooden houses / apartment buildings with overhanging balconies), this one is the most famous (or infamous). The wikipedia article is here: http://en.wikipedia.org/wiki/Great_Fire_of_Rome, although it's not very informative. Tacitus provides a particularly good description, which you can find in translation here (book 15, paragraph 38): http://mcadams.posc.mu.edu/txt/ah/Tacitus/TacitusAnnals15.html

Many believed (in my opinion, erroneously) that Nero started the fire to rebuild the city and make room for his urban villa / palace, the Domus Aurea. The historian Cassius Dio, writing a few centuries removed from the actual events, says,

Accordingly he secretly sent out men who pretended to be drunk or engaged in other kinds of mischief, and caused them at first to set fire to one or two or even several buildings in different parts of the city, so that people were at their wits' end, not being able to find any beginning of the trouble nor to put an end to it, though they constantly were aware of many strange sights and sounds (Dio 62.16).

Suetonius has a similar description:

For under cover of displeasure at the ugliness of the old buildings and the narrow, crooked streets, he set fire to the city so openly that several ex-consuls did not venture to lay hands on his chamberlains although they caught them on their estates with tow and fire-brands, while some granaries near the Golden House, whose room he particularly desired, were demolished by engines of war and then set on fire, because their walls were of stone (Suetonius Nero 38).

Both Tacitus and Suetonius mention that Nero was believed to have sung a poem about Troy from a tower in the safety of the Gardens of Maecenas (on the Esquiline Hill). This also probably isn't true...Tacitus doesn't seem to believe it, since he places the rumor after a description of Nero's efforts to help his displaced citizens after the fire:

Nero at this time was at Antium, and did not return to Rome until the fire approached his house, which he had built to connect the palace with the gardens of Maecenas. It could not, however, be stopped from devouring the palace, the house, and everything around it. However, to relieve the people, driven out homeless as they were, he threw open to them the Campus Martius and the public buildings of Agrippa, and even his own gardens, and raised temporary structures to receive the destitute multitude. Supplies of food were brought up from Ostia and the neighbouring towns, and the price of corn was reduced to three sesterces a peck. These acts, though popular, produced no effect, since a rumour had gone forth everywhere that, at the very time when the city was in flames, the emperor appeared on a private stage and sang of the destruction of Troy, comparing present misfortunes with the calamities of antiquity (Tacitus Annals 15.39).

If Tacitus doesn't believe it (he's the most cynical about the evil of empire and emperors), it's probably not true. And it's highly doubtful that after nearly finishing his first palace, the Domus Transitoria, Nero would have burnt the thing down. However, Edward Champlin, a reputable Nero scholar, actually believes that he did set the fire...it's in his book Nero (Belknap Press 2003), if you're interested.

You may know of this incident because Nero responded to the accusations by mounting the first systematic persecution of the Christians in Rome. We only really have this in Tacitus:

Consequently, to get rid of the report, Nero fastened the guilt and inflicted the most exquisite tortures on a class hated for their abominations, called Christians by the populace. Christus, from whom the name had its origin, suffered the extreme penalty during the reign of Tiberius at the hands of one of our procurators, Pontius Pilatus, and a most mischievous superstition, thus checked for the moment, again broke out not only in Judaea, the first source of the evil, but even in Rome, where all things hideous and shameful from every part of the world find their centre and become popular. Accordingly, an arrest was first made of all who pleaded guilty; then, upon their information, an immense multitude was convicted, not so much of the crime of firing the city, as of hatred against mankind (Tacitus Annals 15.44).

The Romans clearly didn't like them. At the time, they were a pretty small cult, but Nero definitely messed with the wrong people, and they (along with Nero's successors) made sure he was known as one of the worst emperors in Rome's history.

Here are the links to the Dio and Suetonius translations, if you're interested:

Dio: http://penelope.uchicago.edu/Thayer/E/Roman/Texts/Cassius_Dio/62*.html

Suetonius: http://penelope.uchicago.edu/Thayer/E/Roman/Texts/Suetonius/12Caesars/Nero*.html

Also, where any right? If so which ones

Wasn't there some kind of controversi about Alexander (the Great)'s death? If I recall correctly some sources suspect him to have died from poison whereas others believed he had died from malaria. Sorry, I'm not an expert but I thought it was worth mentioning.