One of my favorite theme songs ever is Gilmore Girls' "Where You Lead" by Carole King.
Naturally, I also remember the theme songs that make me think of shows I watched when I was younger:
"I'm Always Here" from Baywatch
Probably one of the most famous theme songs ever: "I'll Be There for You" by The Rembrandts for Friends
And, of course, from one of my favorite shows ever, Charmed (seasons 1 to 3), "How Soon is Now?".
Funny side note - I always used to sing:
"See I've already waited too long
and all my hope is Prue."
because I'm a dork.
Moving on to films, I absolutely love the Harry Potter theme, because it's just so classic and very distinctive to me.
The intro to this movie (My Best Friend's Wedding) is actually my favorite part of the movie, apart from that, I don't really like the rest much. But that song and that video totally rock!
Wonder what movie that song is from?
"Maneater" from Runaway Bride
One last song though: Even though this is a very incomplete and personal list, I have to absolutely include one of the James Bond theme songs. God, I love those themes!