Tom and Jerry annoyed me, as I always wanted Tom to catch and devour Jerry. Ditto Sylvester and Tweety Pie.
Some of the cartoons I grew up with:
Count Duckula:
Funny Bones:
He-Man:
Inspector Gadget:
The Raccoons:
Sharky & George:
Teenage Mutant 'Hero' Turtles:
Thundercats: