I prefer Japanese audio with subs, as you get what is meant to be said, and not what fits the lip movements.
I'd say you don't truly get what's meant to be said unless you actually understand Japanese. When you're reading subtitles, you get text (with some degree of localization, no matter what kind of release you're watching) that's designed to fit within a certain amount of screen space and to be readable within the allotted time. Yeah, some sacrifices have to be made to fit lip flaps, but it's better than ignoring lip movements entirely and winding up with, "Oh! It is Godzilla! We must flee the city! *close*open*close*open*"
Anyway, now for something completely different, by which I mean "on-topic"...
The best, in no particular order:
Cowboy Bebop
FLCL
ROD TV
Ghost Stories (the dub that almost single-handedly converted me from a dub-hating purist to a more "middle of the road" stance)
Kamichu!
Kanon (2006)
Big O
Nerima Daikon Brothers
Desert Punk
Magikano
Haibane Renmei
Koi Kaze
Fullmetal Alchemist (people seem to either love or hate this one)
The El Hazard franchise
Planetes
Wolf's Rain
Dubs that do a good job of improving on the source material: (That is, you probably won't like these if you value fidelity to the original Japanese dialogue)
Generator Gawl
E's Otherwise
Orphen/Orphen Revenge
Wedding Peach
Eden's Bowy
Gantz
Ikki Tousen
Girls Bravo
Negima (2005)
s-CRY-ed
Colorful
Cromartie High
Yumeria
And finally, the worst: (because yes, there are dubs that even
I don't like)
Love Hina
Crest of the Stars
Fantastic Children
Petite Princess Yucie
Kaleido Star (a lot of dub fans like this one, but I could never get into it. Maybe I'll give it more of a shot next time around)
Gravitation
Happy Lesson (they apparently thought the main character's name sounds like a snack product)
Green Green
Risky/Safety (a perfect example of why you don't want to be
too faithful to the original Japanese track)
Kimagure Orange Road Movie #2 (the rest was released sub-only)
Maze TV
Lastly, in the "so terrible it's comedy gold" category: Garzey's Wing.