Hmm... I think these are my favourite animes:
Digimon (First Series):
This anime has left so big mark in me so this had to be on my list. The best thing about Digimon is its musics. Everything from Butter-Fly to Brave Heart. I just loved this. And notice, only the first series. And of course i mean to say the japanese version of Digimon, NOT the english version.
One Piece:
Well if I've watched almost 450 episodes of this anime it has to be good. I just frigging love this anime. Best of this anime are the characters. Everytime Luffy or Zoro starts to fight some badazz enemies (example, CP9) I just get pumped up. The characters are great, storyline is awesome and the music is superb. So please, makess of One Piece. Keep Going!
Death Note:
This is the anime that everyone should watch. If you haven't seen this one, you haven't seen anything yet. Death Note is an amazing example that what animes should be like. Watch this one if you still haven't!
Toradora!
Well , well, well, what do we have here! In my opinion, Toradora! is one of the best Romantic/Comedy animes ever. If your genre is Romantic/Comedy you should watch this one. Every episode is one of a kind.