Azumanga daioh, Inuyasha, Pokemon.

Pokemon, after the time and when I'm getting 12, I relaized that the Anime actually sucks.
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Digimon is purely epic and I love it. I just hate the 5th season. :E
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Monster Rancher (somebody knows this?) was simply great and cool to watch.
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Cardcaptor Sakura, some people laugh me out when I told that I watch this, but I really liked it.

Seriously, screw that Inuyasha, Yugioh! (well the first or 2nd season wasn't bad so) and DBZ crap. =w=

Astroboy <3

Speed Racer, Pokemon, Sailor Moon, Cardcaptor Sakura, Digimon and Magic Knight Rayearth

Dragon Ball GT QAQ

And Clannad.

Trigun and Rurouni Kenshin... I loved both, watching Rurouni Kenshin everyday on Toonami, then Trigun every night on Adult Swim. FLCL and Cowboy Bebop was also great. I don't think Samurai Champloo was around yet in Summer 2003. I watched DBZ and Pokemon before these of course, but they weren't the shows that made me love the anime genre.

Mine were Dragonball and Digimon ^^

Best one for me: Zatch Bell! (Or Konjiki no Gasshu!!)