What were Tacitus' reasons for writing the Annals?

The main motivation behind Tacitus' writing of the Annals was his horror and disgust at the decadence of the Roman empire. Tacitus himself was not only a stern moralist but also a meticulous prose stylist, who, like George Orwell centuries later, saw the decline of culture and language as connected to the decline of civic morality. His rejection of luxuriant Asianist excesses of literary style, and his own concise, unadorned, and even elliptical prose were part of a general disgust with the decadence of Rome under some of its worst emperors. 

The Annales documents in merciless detail the corruption and decadence of Tiberius, Caligula, Claudius, and Nero, connecting their lust for power with their equally unrestrained physical lusts for food and sex (often of a particularly depraved variety -- in the case of Tiberius, pedophilia was just the beginning of a very long list of forms of depravity). 

Tacitus sees murder, torture, matricide, pedophilia, betrayal, rape, and other forms of decadence not only as personal excesses but as the natural outcome of despotism. In his portrait of the decline of the Roman Empire's moral nature, he is arguing that the Republic bred people of better moral stature than the empire and is arguing for moral and political reform.