Since there's already a thread for instrumentals, I thought I'd start this one:

The Flintstones ("Meet the Flintstones")
The Bugs Bunny Show
Yogi Bear
Magilla Gorilla
Top Cat
Howdy Doody
The Beverly Hillbillies
Petticoat Junction
Mister Ed
The Addams Family
Gilligan's Island
Flipper
F Troop
Daniel Boone
The Roy Rogers Show ("Happy Trails")
George of the Jungle
Spider-Man ('60s cartoon)
Huckleberry Hound
Road Runner
Underdog
Gidget
The Monkees
Car 54, Where Are You?
It's About Time
Bat Masterson
Have Gun Will Travel
Archie
Josie & the Pussycats
The Greatest American Hero ("Believe It or Not")
Welcome Back, Kotter
Happy Days
Laverne & Shirley
One Day at a Time
All in the Family
Chico and the Man
Beany & Cecil
Tennessee Tuxedo
Quick Draw McGraw
Wally Gator
King Leonardo & His Short Subjects
The Real McCoys
The Life and Legend of Wyatt Earp
Zorro
Family Ties
BJ and the Bear
Dukes of Hazzard
7th Heaven
Baywatch ("I'm Always Here")
Ally McBeal ("Searchin' My Soul")
Felicity (Season 2)
Frasier (closing theme "Tossed Salads & Scrambled Eggs")
Roswell ("Here with Me")
Smallville ("Save Me")
Summerland
Touched by an Angel

I have many, but the first one that came to mind was Xena: Warrior Princess. The Bulgarian choir was perfect for Xena; it was beautiful and tribal.