These lucky anime titles have been viewed in their entirety by yours truly.

Seen all Rating Comment
20th Century Boys (live-action movie) Very good
3x3 Eyes (OAV) So-so
3x3 Eyes Seima Densetsu (OAV) So-so
91 Days (TV) Very good
Akira (movie) Decent An anime classic with plenty of large-scale visuals and interesting elements... that have already been done before. Akira doesn't do a good enough job explaining, or even hinting, at its more complicated aspects, and settles for visual wonder and trippy, bizarre scenes to justify its mysterious namesake and the powers protecting it. It's worth seeing for the milestone it set for anime films of its time, but it somehow lacks the integrity of previous sci-fi titles, and certainly the manga from which it's based.
Android Kikaider - The Animation (TV) So-so
(The) Animatrix (OAV) Decent (dub & sub)
Appleseed (movie) Good A decent action flick with some interesting ideas and exciting action scenes, but it doesn't excel in any particular area, and moreover, has its share of bad melodrama and ponderous plot elements. The CG isn't great either. The soundtrack is probably the highlight, with tracks by Basement Jaxx, Boom Boom Satelites, and others.
Armitage III: Poly-Matrix (movie) Good
Armitage: Dual-Matrix (movie) Decent
Babel II (OAV)
Baccano! (TV) Masterpiece http://bit.ly/2nruxK7
Batman: Gotham Knight (movie) Decent
Battle Angel (OAV) Decent
Battle Athletes (OAV) Awful
Be Forever Yamato (movie) Decent Probably the most ridiculously implausible storylines (even for Yamato), with a lot of over-the-top elements. However, also very fun, even if it takes itself way too seriously. Visually, it's gorgeous, even for today. Miyagawa's score is, of course, excellent.
(The) Big O (TV) Decent (sub), Very good (dub) Big O is an interesting blend of retro-futuristic mecha action and mystery, with a snappy, often jazzy soundtrack and an art and a style reminiscent of Batman: The Animated Series (which was also partly animated by Sunrise). The series was popular enough in the United States for Adult Swim to finance a second season, with mixed results. Despite a bizarre, hurried ending and a change of style in the animation, the second season fares decently. Overall, the series is worth the price of admission, even if you might not feel completely satisfied by the end. An OVA chaser might work. I'm begging you, Sunrise.
Big Order (TV) Not really good
Big Wars (movie) Weak
Birth (OAV) Decent
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