Well... I've started watching anime about 2 years ago. And now I'm full. It was something new and special for me.
Still my favorite ones are:
1) Neon Genesis Evangelion - this one is.... well it changed me... probably for worse but it did :fool"
2) Furi Kuri - this one is pretty "kind" but crazy %)
3) Excel Saga - heh.. not that kind but much more crazy
4) The Melancholy Of Haruhi Sudzumia - still makes me smile when I think about it
5) Kachou Ouji
6) xxxHolic - no it's not some adult movie =)) It's very mystic I would say.
7) Lucky Star
Azumanga Daiho

7 and 8 are well. This is anime about schoolgirls. But the style is something undescribable.
My first impression on Lucky Star was "no sane person would want to watch THAT!". Well the first episode moslty concentrated on the problem "which side of the cream tube is the proper one to start eating?" And yes there is no plot in general. The whole series are like that =))