As a child I can remember watching The Beatles cartoons on TV.
I don’t think they’ve ever been officially released. This six DVD set is decidedly dodgy, but it contains every episode, plus the sing-along “bouncing ball” songs, trailers and intro’s and outro’s as extras:
The discs are fairly obviously burned onto printable blank DVDs (read: “manufactured at home”), but they are of a reasonable quality and the makers have gone to a little bit of trouble with the graphics:
The quality on screen is similar (possibly even a little bit better) to this example on YouTube:
Rolling Stone magazine has a good article on the background to The Beatles TV cartoon series.