GitS was good, but the Manga is quite long and “sillier” than the movies/television shows. Extensive fanservice… unless you’re big on Manga and advocate it over anything animated, GitS has better treatment via animation.
Akira’s manga was full color, a rarity. Also very long. What you saw in the film happens in the first 8 volumes or so? Then there’s the whole story about what happens AFTER (safe for spoilers) “the ending” of Akira the film.
Azumanga can be summed up well in the anime.
The Melancholy of Haruhi Suzumiya is epic anime/manga alike. Season 2 of Haruhi’s on the way for this fall in Japan/Fansubbers.
Ranma 1/2 lasts forever, both manga and anime, but the anime only follows the manga up to about Season 2 or 3: From there it’s very modified, coming back to the manga every now and again.
Fist of the North Star lasts for freaking ever, Manga and Anime. The Fist of the North Star anime films are good, with the original being one you’d have to see to believe. Even people who aren’t anime fans love that movie.
Inuyasha… lasts forever. Also follows the manga up to a point, then becomes a bunch of gibberish for a few DOZEN episodes.
Bleach is the same way. First two seasons are really the only ones worth watching, then I lost interest (story became way too bland).
Naruto suffers the same fate. First 2–3 Seasons are great, then the next HUNDRED episodes or so you could live without. They throw in little tastes of the main story here and there, but it’s mainly “Hi! I’m still in this anime!” cameos for awhile. Shippunden (or whatever) ages the characters a bit and pushes the story ahead a few years and is great for a few episodes, but quickly falters.
Dragonball Z… skip it. Also lasts for freaking ever. In the anime? 3 episodes can go by where Goku’s chargin’ his lazer before he throws it at something… and misses. Season finale’s when Goku dies, season premiere’s when Goku comes back to life.
“Battle Angel Alita” was the name of an anime based on a Manga, the original name slips me at the moment, but it was something like Gunnm (Not Gundam). The anime was piss poor, but the Manga’s definitely where it’s at.
Golgo 13 has extensive life in Manga, and the anime can’t be missed either.
And finally… the mother of ‘em all…
Lupin the 3rd. The anime lasts a few hundred episodes, the combined weight of all the manga probably weighs more than most encyclopedia sets and is probably one of the funnest anime/manga you can get into. Before EVERYONE knew who Hayao Miyazaki was (thanks to the DISNEY deal), even Miyazaki covered Lupin the 3rd with the terrific film Castle of Cagliostro.
…is my fanboy side showing? Lemme tuck that back in.