the maiestas trials were a common theme in Rome's history, although they were most prominent in the fall of the republic and the imperial period
i only did augustus and the julio claudians, so i can only provide details on that time period
Augustus - contrary to popular (senatorial) belief, during Augustus's reign maiestas trials occured, and many senators who did not support augustus, his heirs, and were against him in the civil war faced the maiestas trials
Tiberius - most known for his use of the maiestas trials, he through sejanus, conducted a severe period of maiestas trials...you could argue, that since most of the senate hated tiberius, the source material that we based this information off (senatorial records) is misleading.
Gaius - he also used maiestas trials to consolidate his power after the first 6 months of his reign (when he supposedly went crazy) a general point can be said here: most emperors used the maiestas trials to consolidate their political power (most of the time in the middle of their rule, since they were generally quite positive to the senate in the beginning of their reign)
Claudius - had some, and the ones that he did have were expounded by the sentatorial records as they were hostile towards him for setting up the imperial bureaucracy and giving too much power to his servants: Narcissus, Pallas and Callistas
Nero - not much during the five good years (Nerois quinquennium - i think thats the spelling) but after agrippina, seneca and burrus died or retired, they began again.