Claudius, a dweeb disrespected by his peers, and unironically one of the men most responsible for the Roman Empire as we know it today. It was his influence which opened the positions of power to provincials and formalized the auxiliaries as a means of assimilating new Roman citizens. He genuinely regarded himself as part of the Senate, and not a god or pseudo-king. He had a famously strong sense of justice, sparing enemies and punishing friends even when it would have been more beneficial to pursue injustice. He greatly expanded infrastructure in Italy and implemented many economic measures to stabilize the Empire-wide economy and encourage the free flow of trade which bound the Empire together by common interest. He considered the bedroom habits of other citizens to be none of his business (though he himself was noted to like only women - not usual for the Roman elite!). He was a scholar of history, an obsessive nerd, a stutterer, and a cripple, so he just like me fr fr. He's my spirit animal and I love him.
Trajan was a wise and fair Emperor who conquered Dacia and temporarily conquered Persia (he died of natural causes before he could finish). He implemented welfare policies for the poor and orphans, embarked on massive building projects, opened the Senate to a wider array of citizens, and implemented reforms of local government to improve its efficiency and responsiveness to local needs. He greatly respected the Senate and was quick to bow to their wishes, despite the fact that his overwhelming popularity and power amongst the army and people would have allowed him to run roughshod over the Senate if he were a different man (and as many less restrained Emperors did).
Antoninus Pius, an Emperor who ruled over a period of unprecedented peace and prosperity, reforming laws to favor mercy and the presumption of innocence, safeguarding the rights of the weak and investing in infrastructure, all while maintaining a massive budget surplus. He put Christians (until then sporadically persecuted by local authorities, who found their customs strange and incomprehensible) under the personal protection of the Emperor, as he saw the cult as harmless (or at least no more harmful than any other). He was attentive to affairs of state up until the very day of his death, and treated himself as the Emperor was supposed to be - simply a magistrate, an official serving at the pleasure of the Senate and People. He loved his wife deeply, and raised his adoptive sons well (Marcus Aurelius and Lucius Verus), with both of them turning out reasonably well-adjusted human beings who remembered him fondly as a man who took them fishing, and to see plays and boxing matches. "Did nothing, but did it excellently" is a somewhat memetic descriptor of his reign, but it has some accuracy to it - Pius made sure his extraordinarily long reign as Emperor was quiet and peaceful.
For some of my SPICIER takes:
Augustus gets remembered mostly for being the first Emperor and a top-notch politician/propagandist. He was competent, but many of the precedents he set were mixed or set aside, and his major policy successes were only in shoring up his own power - neutering the Senate, and eliminating all other centers of power to create the pseudo-dictatorship of the early Empire. He is not the titan amongst Emperors he is often portrayed as. Propaganda works, boys and girls, even 2000 years later!
Tiberius, sad boi extraordinaire, gets largely tarred by the trials of his later reign. He quite literally did not want to be Emperor, but Augustus was very insistent, and one does not easily refuse an autocrat. But Tiberius was a very competent administrator who paid close attention to the economy and repeatedly tried to make the Senate (by then filled with Augustus's bootlicks who were more interested in sycophancy than government work) more involved in the rule of the Empire. After a while, big shock, the man who didn't want to be Emperor simply... stopped being Emperor. Went off to a private island, one supposes thinking that the Senate would just rule in his absence. Instead, they basically were couped by a handful of soldiers in togas, and let the coup leader plot to murder Tiberius until he caught wind of it and reluctantly dragged himself back to Rome to see the conspirators executed.
Marcus Aurelius was simply a competent workaholic. He was a bitchin' philosopher though, and for that reason, is often regarded much more positively, I think, than his rule deserves.