Youtube user dotflist has a playlist collecting classic TV themes and openings ....except something seems to be slightly off
The Okeh Laughing Record, a novelty recording, was first released in 1923 and rose to #8 on the Billboard charts, becoming the highest ranking anonymous* recording ever. It's history and provenance is completely unknown**. It has since appeared as the soundtrack to cartoons, on Dr. Demento and on Jean Shepard's radio show. [more inside]
Willy Bum Bum. Not safe for anything, really (cartoon willies and bums).
The Counting Song (SLYT), a cute, animated ditty for kids that may be too educational. From Adam Buxton (previously here)
Less Than Three... oh emm gee. [SLYT]