Your choices include ...
THE FLINTSTONES (1960)
THE DEPUTY DAWG SHOW (1960)
THE ALVIN SHOW (1961)
THE BULLWINKLE SHOW (1961)
THE YOGI BEAR SHOW (1961)
TOP CAT (1961)
ASTRO BOY (1963)
THE JETSONS (1963)
JONNY QUEST (1964)
THE UNDERDOG SHOW (1964)
THE BEATLES (1965)
THE ARCHIE SHOW (1968)
SCOOBY-DOO, WHERE ARE YOU? (1969)

scooby doo...although i associate it more with 70's

2nd choice would be the flinstones

The original Jonny Quest

Your choices include ...
THE FLINTSTONES (1960)
THE DEPUTY DAWG SHOW (1960)
THE ALVIN SHOW (1961)
THE BULLWINKLE SHOW (1961)
THE YOGI BEAR SHOW (1961)
TOP CAT (1961)
ASTRO BOY (1963)
THE JETSONS (1963)
JONNY QUEST (1964)
THE UNDERDOG SHOW (1964)
THE BEATLES (1965)
THE ARCHIE SHOW (1968)
SCOOBY-DOO, WHERE ARE YOU? (1969)


In no particular order:

The Flintstones*
The Bullwinkle Show*
Top Cat*
The Jetsons*
The Underdog Show
Jonny Quest
The Archie Show
Scooby-Doo, Where Are You?

You forgot "The Huckleberry Hound Show" which I own on DVD. :)

*Own series on DVD

Alvin Show I've seen in various snippets (maybe an episode or two)
I don't think I've heard of Astro-Boy
The Beatles cartoon series (no station or cable channel picked them up). :(

No, I didn't forget HUCKLEBERRY HOUND (which is probably my all-time favorite).
But it began in 1958 (although it did last into the early sixties), and I was
compiling my list based on the date the show began. So I'd put that under
the 1950s.

THE BEATLES was on ABC for three seasons (1965-1968). Later it was
syndicated and also aired on MTV and, I think, the Disney Channel.

the Archie show...it was so bad , it was good.....they didnt even get the car right :p