I use to watch a cartoon movie- probably made in early 80's about a bear family and they sang a whole bunch of nursery rhymes like rain rain go away and I think London bridges... the baby bear was peabody and also a cartoon movie about safety- it had songs about not talking to strangers, what to do in case of a fire etc... Does anyone know the names of these?

The Beary Family? Tough to find:
http://www.youtube.com/watch?v=gWu0Irjgt8I

I know what VHS video you are referring to, but unfortunately I am on the same quest as yourself. I do remember the little bear named Peabody. Wasn't the older sister named Sara?

I think it is titled "A Golden Book Music Video" and it is about the bear family. It contains the songs: 1.The Old Woman Who Lived in a Shoe, 2. Hickory, ory, Dock, 3. Pease Porridge Hot, 4. Here We Go Round the Mulberry Bush, 5. The Alphabet Song, 6. One, Two, Buckle My Shoe, 7. London Bridge is Falling Down, 8. Lavender Blue, 9. I'm a Little Teapot, 10. Rain, Rain, Go Away, 11. Diddle, Diddle Dumpling, 12. Hush, Little Baby


I found the VHS on Etsy:
A Classic A Golden Book Music Video 25 VHS 1st by SashasPrissyPaws

Youtube vid of the intro:
Golden Book Video - A Child's First Nursery Songs - part 1 - YouTube