Of the various Henson Company theme songs, my favorites are the ones from The Muppet Show and The Jim Henson Hour.
When it comes to theme songs from animated shows, I like the themes from Teenage Mutant Ninja Turtles (the original theme for the original series), Animaniacs, Rugrats, Rocky and His Friends (I've read that some of the music for the series was replaced on DVD, so I don't know if that music is what was originally heard - but I also like the Bullwinkle Show music), Family Guy, The Cleveland Show, Taz-Mania, Hamtarro (both the opening and closing), Pokemon, and DuckTales. And of course I really like the classic Looney Tunes theme music, as well as the "This is It" theme from The Bugs Bunny Show and other television packages.
I also really like a lot of '80s theme songs, including Small Wonder, Newhart, Mr. Belvedere, Perfect Strangers, Three's a Crowd, Family Ties, Growing Pains, Making a Living, and Eight is Enough. And quite a few of the shows on this list are ones that I haven't watched much (though there was a brief time last year when I tried to watch Mr. Belvedere quite a bit), if at all (Making a Living is the only one that I've never watched).
Speaking of themes I like for shows I haven't really watched, I really like the theme songs for Daniel Boone and Matlock.
And when it comes to classic TV shows (that I have watched regularly), I am a big fan of the themes for Mary Tyler Moore, The Dick Van Dyke Show, The Bob Newhart Show, Diff'rent Strokes, Rhoda, and Sanford and Son. When it comes to more recent shows (let's say shows introduced around the early 1990s), I like the themes for Salute Your Shorts, The Red Green Show, That '70s Show, Greg the Bunny, and How I Met Your Mother.