According to this commentator, the traditional rhyme "London Bridge is Falling Down" references the pagan custom of ritually sacrificing a young (human) victim at the occasion of building a bridge.

After I grew up, I wondered why in the hell parents read these horrible stories to their sweet children. I never read them to mine. So, I've probably deprived them of part of common knowledge, but I just couldn't do it.

I recently heard this for the first time from the director of the co-op where I take my daughter. And I thought I knew about all the violent nursery rhymes!

"London Bridges," to my recollection, was about the inprisonment of one of the English queens. I don't recall any historical info about pagans sacrificing anyone to dedicate a building.

"Ring Around the Rosy" was about the black plague.