Here are some of my favorite songs for teaching children about counting numbers:
Zero by They Might Be Giants
The Batty Bat sung by Count von Count, focuses on the numbers 1,2,3.
Feist sings 1,2,3,4 on Sesame Street.
High Five! by They Might Be Giants.
The Secret Life of 6 by They Might Be Giants.
The Alligator King is a special song for counting to seven, from Sesame Street.
King of 8 is a snappy song for counting to eight, from Sesame Street.
Figure Eight by They Might Be Giants (This is great for thinking about the shape and seeing the difference between 8 and 9; this is commonly confused with dyslexia).
Pirate Girls Nine by They Might Be Giants
Pentatonix counts and sings to twelve with an a cappella focus on the first five numbers, on Sesame Street.
One Dozen Monkeys by They Might Be Giants (staring Hannah Levine).