Im very curious and i feel this is a very important topic to understand human nature and social evolution. Were there ''memes'' in roman times? Or any kind of social phenomenon that could be related to memes? I understand that the lack of internet can limit the viral part of the meme spread.
PS: Im not trolling.
I hope people do not take this as a joke but religions and gods specifically are memes. So yes.
I'm not sure if this counts, but there was definitely graffiti. We have books of quotes from the walls of Pompeii. You can see some of these in the Latin-learning textbook Scriblers, Sculptors, and Scribes, meant to accompany Wheelock's Latin.
As far as graffiti "going viral" (again, not the same thing as a meme), there's a story about an oft-repeated phrase during the "Arian Controversy," circa 325 CE. This was a debate in Eastern Rome about whether the second person of the Trinity was eternal, or just really old, begotten or unbegotten, whether God somehow "gave birth" to his son or whether the son always existed. [Edit: I went back to my notes from my MA!] Apparently the Arians started writing "there was a time when he was not" on the walls everywhere, and the Proto-Nicean Anti-Arians just threw an "ouk" before it, negating the whole sentence to "there was no time when he was not."