Leaders used to have nicknames, (The Great, The Terrible, The Meek), but it seems, at least in the western world, that disappeared. Do we know why? Who was the first major head of state to go without it? Or was the nickname given to them posthumously, and that tradition went away?

While more can always be said, this previous answer of mine, I think, gets to the heart of what you're asking about, with some additional information from /u/AlviseFalier about the naming system in Italy.

A couple of clarifications: where I wrote "1100s-1300s", I probably should have written "1100s-1600s" because it wasn't until the late 16th or early 17th Centuries--when parish baptism records became compulsory--that the modern form of surnames became nearly universal in England, though it was already a common practice by the end of the 1300s. Parts of France began adopting them around the same time, while the rest of Europe adopted them later, anywhere from the 1500s to 1800s, but Catholic countries mostly adopted them in the late 1500s and early 1600s with the introduction of baptism records in their parish churches. The fixed surname practice spread throughout the rest of Europe from there.

Someone may also point out the use of ekenames, which was more or less just a synonym for byname until baptismal record-keeping, and the later connotation of ekename as a forerunner of the modern word nickname can add some confusion--or maybe it adds some additional context, depending on your view. In any case, according to the Oxford English Dictionary, both terms first turned up in the English language in the 14th Century, and they stick to the word byname in The Oxford Dictionary of Family Names in Britain and Ireland, so that's the word I used in that previous answer.

For some additional context, you may want to just go ahead read the introduction of The Oxford Dictionary of Family Names in Britain and Ireland, especially starting with the section headed "What is a Family Name?".

TL;DR: Those nicknames were called bynames, which were an older form of "last name" before fixed surnames or family names became widespread. As nobility adopted fixed family names, the older system of bynames went out of use. The peasantry also used bynames, though theirs wouldn't really be "the Great" or "the Terrible", but things like "the Smith" and "the Brown". The peasantry also came to use fixed surnames, and the use of the older byname system became obsolete. This happened at various times throughout Europe, but mostly between the 1100s and 1600s, with some stragglers not using a true fixed system until the 1800s. And even today, Iceland still does not, though they don't use the byname system, either, but they instead use an older alternative to fixed surnames, which is referred to as patronymic names.

With nobility specifically, they all had some common byname in use at the time they were alive ("William of Normandy") but they often gained additional nicknames either through their life or after they died ("William the Conqueror", "William the Bastard") so not to confuse them with their offspring or other historical figures with their same first name and byname. But the history of the use of any specific name varies depending on the historical figure being referred to. It may have been something in use while they were alive, and it may have been something that doesn't show up in the historical record until after they died, depending on the person.