A few repetitious songs that children in my class enjoy singing are:

The Wheels on the bus

The ants go marching

Open Shut Them

Hey Diddle Diddle

Two Little Blackbirds

BaaBaa Black Sheep

The Muffin Man

Hicory Dickory Dock

Five Little Monkeys Jumping the Bed

Five Little Monkeys Swinging in the Tree

Four Little Ducks

Ten Little Indians

Down by the merry old pond

Bingo

The Farmer and the Dell