Japanese
my experience is pretty limited consider how big a nerd i am, but of what i've seen:
Ghost in The Shell - movies and TV series. it might help going in to know(if you don't already) that the the original movie and its sequel are sort of "AU" to the series Stand Alone Complex and ITS follow-up movie Solid State Society(which takes place after Season 2, SAC: 2nd Gig).
Trigun - good, but the manga was still going when the anime ended. that said, they did a better job than most "wrapping it up." (seriously, "new shoes?" WTF, man, W.T.F?)
Cowboy Bebop
Outlaw Star - a typical action anime, but it meets the criteria.
Fullmetal Alchemist - there are actually two anime based on the same manga, and they are both quite different. the first, simply called Fullmetal Alchemist, starts off in -line with the manga, but then, as is want to happen, outruns the manga and everything after the first act is more-or-less entirely the work of the studio writers. despite this it's still very good. The second series, FMA: Brotherhood, is more a translation of the manga than and adaptation. the overall animation, however, isn't as good in my opinion.
Gundam - pretty much any of the various gundam series up to Gundam Wing, especially the OVAs. I haven't seen any of the more recent incarnations(i saw G-Gundam, but i forget if that came later or not), so i can't comment, but i can say the artwork i've seen from Seed and 00 seems a lot more generic than their predecessors.
Rurouni Kenshin - a fairly typical shounen anime, but if you like that genre it's among the best in my admitedly-limited experience. it does have the distincion of better-than-average character development and relationships that actually develop as the series progresses, as opposed to coming out of nowhere for, worse still, the "harem" genre. only problem here is that the manga is greatly superior. it's another example of an anime ending while the manga was still going, with the whole third season being filler. they did make two OVAs, Reflection and Remembrance,which cover most of the third manga arc's plot, but ends the story VERY differently to how the manga author did, so much so that he has outright rejected it as canon. it's still well-written, and fits with the tone set in the OVA, but if watched back-to-back with the anime you'll find yourself wondering just what the hell happened to everybody to make them all into living Prozac ads. the manga ending sees the characters in a place much more consistent with how we've seen them grow.
Now, one thing these all have in common is the dubbing; they all range from pretty darn good to fan-frakking-tastic. this is really good as it means you can focus more on the animation than if you were having to read all the dialogue. the one exception to this is, sadly, Kenshin. it starts out pretty good, but it starts slipping a bit in the Kyoto Arc, and in little i've seen of the final filler arc it's downright sub-par(bottom line: if you decide to check out Rurouni Kenshin, get the manga instead).
American
Batman TAS
and just watch this video:
Top 11 American Anime
Dragonball Z is certainly epic, but you really need to be in the target age range to actually enjoy it. i still had to mention it, just for the nostalgia. the original Dragonball is pretty good though, but look for it uncut.