I admit I have very little experience with anime, however Cowboy Beebop has given me a respect for it. Heck, the soundtrack alone is epic, the opening track "Tank" is alone is worth the price of admission.
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The only ones I've watch were on adult swim. .hack//sign, then Ghost in the Shell, then Cowbot Bebop and Samurai Champloo. Gee, almost forgot Bleach. That one went on for years. One episode a week. Great ending though.