I'm one of those borderline anime fans, never have gotten into the ones that lay the "anime mannerisms" on too thick. Thus my favorites are Cowboy Bebop and FMA. You can't knock FMA's coherent, engaging story... I watch Bleach too, but Bleach likes to jump into too many subplots and gets caught up in prolonged fight scenes. FMA is much better at tying things together and making it feel like a whole.
Bebop is just so artistic, it's a bit of a shame it's so short, but there's something to be said for ending strong. The style was very well defined, and it felt more like a slice of someone's real life than a deliberate storytelling.
I have also seen pieces of Trigun and Escaflowne. Didn't especially care for either one... Escaflowne seemed VERY random, I started from the beginning and still often felt very lost. Trigun lacked believability.