Cookie bear is the original term, before the children's television show Sesame Street, for what is now universally called the cookie monster.

Apparently the term comes from The Andy Williams Show's "Williams' Wierdos" sketches which had a character called "Cookie Bear". In these sketches, a man in a bear suit tried all sorts of tricks to get a cookie out of Williams. The sketches would always end with Williams shrieking, "No cookies! Not now, not ever...NEVER!!!", and the bear sadly wandering offstage.

From the Jargon File 2.4.2 (used by permission)

2: The name of the bear used by Hudsons, then Griffins Foods Limited New Zealand in their marketing of biscuits for many years. A whole generation of New Zealand kids were members of the Cookie Bear club, receiving postcards on their birthday. Cookie Bear Postcards