1) "Born in the woods"
Davy Crockett. No, he was born on a mountaintop. Was Daniel Boone borne in the woods?
2) "any rule, we'll break it"
The Flying Nun
3) "Gee our old LaSalle ran great"
AAAARRRGH! Archie, Edith, Meathead and Gloria. Can't think of the show's name, though.

4) "Here's Kate and the girls and the boys"

5) "Toting my old forty-four"
6) "Yoo Hoo! It's me! My name is _____ ____" (first line)
Not "Pee Wee" was it?
7) "I can be what I want to be and if you'd like to see"
Sounds like PeeWee Herman again. ;-)
8) "Keep smiling until then"
Carol Burnett Show
9) "When he hears this mighty sound"

10) "Land stretching out so far and wide"
Green Acres