TV cartoon theme music of the '60s only, please.
Two of my favorites are Gigantor and Cool McCool. What is yours?
Underdog
Is he strong? Listen, bud: he’s got radioactive blood.
This one, hands down!
I always like Magilla Gorilla’s theme song.
The Gerry Anderson series all had great themes:
The best Hanna-Barbera themes:
It’s got to be that protector of the weak, defender of the innocent, and all-around good guy, George of the Jungle.
No love for The Alvin Show?
KISMET!
I was thinking of Gigantor when I read the title!
Years ago, during a visit to Vegas, I found some Gigantor tapes at SunCoast and to my girlfriend’s horror started singing the theme song to the young clerk.who had no clue what the tapes were. Gigantor, Gigantor, Gigaaaaaaaaannnnnnnnntor… 
Along the same line, other Japanese imports, Astroboy and Speed Racer and I think King Kong was also Japanese. Kiiiing Kong. You know the name of Kiiiiing Kong, 10 times as big as a man…
King Kong,
Oh…and Speed Racer! Go Speed Racer, Go Speed Racer, Go Speed Racer GOOOOOOOOO!
I had such a crush on Trixie! 
Speed Racer:
And, in the original Japanese (which had additional scenes that didn’t appear in the US intro):
But, my favorite Saturday morning show was a mix of live-action and cartoons – The Banana Splits:
Call for Super Chicken!
When someone complains, I still use his catchphrase: “You knew this job was dangerous when you took it!”
The Adventures Of Rocky And Bullwinkle ('59-64)
Dudley Do-Right!
Top Cat.
Johnny Nash sings “The Mighty Hercules”… The Mighty Hercules Opening Theme | THE MIGHTY HERCULES - YouTube
Definitely Gigantor and Underdog. My first, however, was Crusader Rabbit:
I don’t think your first was a cartoon from the '60s.
This. In fact, I can’t think of a theme song to any TV program I like better.
ETA I always wondered what the directions were after those introductory triplets. Trills, mordants, what? This shows…nothing.