As far as I know, barbarians start appearing beginning with 16th turn of the game, so those several hundred/thousand years (depending on difficulty level) are basicaly free of barbarians. Later on, as technologies progress, so do barbarians. Aside from getting more advanced units, they also become more numerous I think, although I remember having large groups of barbs in ancient times as well. I believe there is a maximum number of barbarian units that can show up in one place although less units than the maximum is also possible. Max for Raging Hordes should be about 20.
Another thing is barbarians show up at random. If you save the game, get barbarians appearing randomly at one uninhabited spot then reload the game - you either won't get them again at all or they will appear in an entirely different place, possibly with more or less numerous and different units. Impression that barbs show up more often in late games might be purely random in your situation, you were just lucky to get them later, when they are far more managable than early on.
