In the days of DVD and DVR, we have a tendency to fast-forward through the opening credits of even our favorite TV shows. Sometimes we're better off - for instance, after four seasons of Gossip Girl, we get that there's one secret you'll never tell. But some shows really know how to work their themes into the episode. Perhaps my favorite example of this is the cold open of The Office that shows Michael's reaction to Toby's return - his screaming is so perfectly interrupted by the theme song that we wonder how long it would have otherwise gone on. Dexter's wonderfully creepy opening theme (though two minutes is a bit long) is actually figured into one episode - a scene showing Dexter in his morning routine - instead of being played at the beginning.
Everyone will always remember the classic theme songs - Love Boat, Friends, Sesame Street, Cheers - but I think the best are the ones you can sing along to using just "doo doo doo"s or "bum bum bum"s (even better, ones that are essentially doo doo doos and bum bum bums on their own - How I Met Your Mother, Parks and Recreation, etc.). Or, just one big BUM, as to not interrupt any brilliance at work.
There are also shows whose themes work to their disadvantage. I know someone who refuses to watch Dawson's Creek because they can't make it past Paula Cole. Then there's Two and Half Men, whose theme is (if this is possible) even more grating than the show itself (I'll spare you the links on those ones). But at least those are memorably bad, instead of forgettable. Speaking of which, I dare anyone to hum the theme to Modern Family. Impossible, right? What a waste.