Does anyone else remember the WB cartoon "Detention"? I loved that cartoon, and I personally believe it had a great theme song.
http://www.youtube.com/watch?v=27IxAlmijno
As for anime television shows, some of my favorites include:
The opening for the original Hellsing anime. While the OVA series is superior to the original anime in most regards, the one thing it lacks is the fantastic soundtrack of the original effort.
Another fantastic opening is that for GetBackers, or rather, the second opening them, "Rose Colored World".
http://www.youtube.com/watch?v=81o9JSQiSsw
Another is the opening for Princess Tutu, which I consider to be the BEST magical girl series ever made.
http://www.youtube.com/watch?v=KsipExvcHgM
I've added links to the actual opening videos where I could, as I think it helps to here them and see the images associated with them. I've refrained from posting the one for Hellsing, as it probably would brake the forum's rules for the content that can be posted, as it easily exceeds a PG rating in its imagery.