There are so many violent ones. I didn't really think about it till I had my own kids and started reading them nursery rhymes, and then I thought WTF?!
A lot of them have some historical reference, like Goosey Goosey Gander, which probably relates to persecution of Catholics in the 17th century.
Goosey goosey gander,
Whither shall I wander?
Upstairs and downstairs
And in my lady's chamber.
There I met an old man
Who wouldn't say his prayers,
So I took him by his left leg
And threw him down the stairs.
I have only just looked up the origin of the Three Blind Mice - it seems this is also likely to be religious, this time persecution of Protestants by Queen Mary I.
Three blind mice. Three blind mice.
See how they run. See how they run.
They all ran after the farmer's wife,
Who cut off their tails with a carving knife.
Did you ever see such a sight in your life
As three blind mice?
Strange topics for children's rhymes though!