Wow, so many to choose from it's scary.
the Comic Strip: The catchy, jazzy foxtrot beat, although from the 80s is one I enjoy thuroughly.
SilverHawks: I loved the guitar riff that Bluegrass played in this- it's a shame that theme songs these days aren't as catchy.
ThunderCats: I know I've mentioned pretty much all of Rankin/Bass's 80's cartoon lineup, but you have to admit this is quite catchy.
Jayce and the Wheeled Warriors/Jayce et les Conquerants de la Lumiere: Shuki Levy was a theme song icon! I loved both the English and French adaptations to Jayce and the Wheeled Warriors, especially since Jayce et les Conquerants de la Lumiere had an extended "album" version of the theme song- something that's almost nonexistant in American cartoons.
Come to think of it, pretty much anything that Shuki Levy composed in the 1980s was catchy, like Saturday Supercade, Samurai Pizza Cats and the Super Mario Bros. Super Show! to name a few.
Spartakus and the Sun Beneath the Sea/Les Mondes Engloutis/Pirates Upon the High Seas: not many remember Spartakus and the Sun Beneath the Sea (Les Mondes Engloutis in France), but the show had a calm, relaxing theme song. The Pirates Upon the High Seas, while within the show was upbeat and catchy, both respectively in its native French version and English adaptations.
While not a cartoon, but still under the same category of catchy theme songs, I'd nominate The Great Space Coaster. The Great Space Coaster was Sesame Street with a sci-fi spin, and even though not as well-known as Sesame Street, the theme song was earworm enducing.
the Ren and Stimpy Show: I love the classic, jazzy tune. it's very much reminiscent to the golden age of cartoons.
Lastly, I'd go with Count Duckula and Danger Mouse respectively because they both had equally good theme songs.