A few of my faves...
The Jack Benny Program...several different openings, two different closing themes (the one used for most of the show's run was called the "J & M Stomp," named after Jack & Mary Benny) and a completely different theme for episodes that were rerun in a Sunday afternoon slot as "Sundays With Jack Benny."
Beauty And The Beast (Linda Hamilton and Ron Perlman, respectively)...Completely different open and close themes, though both in the same mood.
Any of the Gerry Anderson "SuperMarionation" puppet shows from the 60's (Stingray, Fireball XL-5, etc.) had very dramatic opening themes and either lively or romantic ("Aquamarina" from Stingray) closing themes.
Sheena, Queen of the Jungle (1950's version starring "Irish" McCalla)...Opening theme more adventure style, end theme angelic-sounding "beautiful girl" music (and she was, too.) Themes credited to one Eli Briskin. Some early episodes available on DVD carry no music credits and used stock music that sounds left over from a sci-fi or horror movie.
Jonny Quest...The same theme but arranged very differently for main and end titles, and one hell of a jazz chart by Hanna-Barbera staff composer Hoyt Curtin. Very Kentonesque style.
The best place to look for TV themes I know of is
http://www.televisiontunes.com/ There are probably You Tube clips of some of these (and others) too.