I just finished watching the second episode of Digimon Adventure (that's the very first season of Digimon). Gosh, how that show brings back childhood memories...

Other anime I'm following now: (in no particular order)

Death Note
Ouran High School Host Club
One Piece
Slayers
Fairy Tail
Nerima Daikon Brothers
Excel Saga
Hellsing

I found out about Nerima Daikon Brothers through my school's anime club. That show is so naughty, but fun and full of music anyway. We're also watching Baccano, which I've found difficult to follow, but has the most amusing couple of thieves ever.