I'll also give a shout out for Ghost In The Shell. The film is one of the better sci-fi films I've seen.
I picked up the book (Dark Horse version) after having seen the film, but didn't find it all that gripping.
Mamoru Oshii's 1995 feature
Ghost in the Shell is very different from the original manga. I would say the movie is on a par with
2001: A Space Odyssey. The TV series
Ghost in the Shell: Stand Alone Complex is closer to the characters and situations in the manga.
Asking "what's good in anime or manga?" is such a wide-open question that one should be aware it is like asking "what's good in Hollywood sci-fi?" I've had certain friends recommend series after series and
completely miss the target on every call. That does not mean the recommendations are bad, just that my tastes are different. Once you find a critic whose taste seems to approximate yours, you can feel more comfortable about jumping in and buying books or DVDs—but don't be afraid to experiment.
Anime on-line is a great option. I also like to check Wikipedia for a little background—any information at all is better than a "blind date" recommendation. Many people above have recommended
Cowboy Bebop. While I enjoyed various aspects of the anime, I would not actually recommend it to anyone as a "must see."
Some people might like the anime
The Melancholy of Haruhi Suzumiya from start to finish, but for me the series bottomed out after the six-part pilot episode (based on the first volume of the light novel series). I like something that invites me to read more deeply. For example, in
Haruhi one of those things is that Haruhi may be
a god, but not
the god. (In fact, I'd say Kyon is the one. Think about it.)
One of my favorite series is
Oh, My Goddess!, both manga and anime. This
seinen manga started in 1988 and is still running. There are two anime series (1993 OVA and 2005), and a feature film. The basic theme is marriage (a college student meets a goddess and asks her to stay by his side forever). I especially like the way the manga mixes modern science with mysticism, e.g. the Maxwell's demon-powered flying broom. One of my favorite story arcs began with the two main characters getting lost in infinity. Only half of this story appeared in the anime. In the second half, the human character meets a Schrödinger's whale. The symbolism in this is really fantastic as the human saves the whales by teaching them to "collapse their wave functions."
Again, check the recommendations, do a little research, watch a few episodes, then follow up the ones you like.
