Darnit! Ae86 beat me to Johnny Bravo!

I used to have the songs for Record of Lodoss War Memorized.

Though I'm not sure how good it really is, I like the old Loony Tunes opening. Must be nostalgia. I can still sing it. :). Mostly. ;)

Right away I think of Rugrats. Not necessarily one of the best. But it's the only one I got interactive with (beyond singing along). When Tommy would squirt his bottle I always tried to dodge it at the last second. xD

Doug! :D

The opening to Kore was Zombie Desu Ka? http://www.youtube.com/watch?v=1GvzCeCt2ek <333 I also recommend this anime as a whole. It's pretty awesome.
And the opening to season 1 of School Rumble. http://www.youtube.com/watch?v=U2NgBrozFi8

5th season opening of Gintama "Donten"-made of so much awesome

It's an ending, not a beginning, but my favorite is Yu Yu Hakusho ending 3.

Doug was clever, I liked that one. Samurai Jack did have a neat sound to it.

One of the Fullmetal alchemist ones, I can't remember which one but it was really good.

I loved one of Mirumo De Pon's endings, but try as I might, I can't find it on Youtube. It's weird o.O;; I know it was one of the very first seasons, but...yeah.

The Animaniacs. It was constantly changing.

Monster high

The first Pokemon opening. :D