In many places in history, regnal dating was essentially the only yearly date that mattered--the current year would've simply been something like "the sixth year of the reign of Kurigalzu II" or "the fifteenth year of the reign of Khasekhemwy." In a place like the Roman Republic, without a king, consuls took on the role--it would've been "the year of the consulship of Appius Claudius Sabinus and Titus Quinctius Capitolinus." A really weird example of this kind of thing is Greek Olympiad dating, in which the names of famous Olympiad victors were used as year dates, although the more usual way of doing it was just the ordinal number of the Olympiad, which is an example of epochal or era dating--for that, back to Rome...

Rome is also an example of the place that had a second, epochal yearly dating system corresponding to the supposed founding date of the city--the ab urbe condita system, although the best evidence suggests that, somewhat surprisingly to the modern eye, this system was important mostly for ritual use, and was not commonly employed by people engaged in everyday business to describe what year it was. Some other areas, like Parthian Iran or the Selucid Empire, also saw use of calendar epochs/eras corresponding to certain large historical events. The Hebrews/Israelites appeared to use, at least for some purposes, epochal year numbering beginning with the Babylonian captivity or the supposed escape from Egypt.

There is some suggestion that, particularly more "locally," ancient people (and even those much later in history) would also employ "folk dating" systems, making haphazard-but-good-enough use of whatever events would've been important and well-remembered in the area--"the year the Severn flooded," or "the year the Circassians sacked the town," or "the year of the great fever."

As to your second question, our AD/BC epochal system comes from Dionysius Exiguus, one of the famous "Scythian Monks," from modern-day Romania. It was slowly adopted in kind of a piecemeal fashion across the Christian world from about the sixth century to the Late Middle Ages or so. Weirdly, in some places, it seems to have replaced a previously-used epochal system called the anno martyrum, which started the numbering at a later and seemingly less important event than Christ's birth--the date of the last major Christian persecution.

hi! you'll find more examples in the FAQ

• Other dating systems