Anime can be hard to get into, especially if you're approaching it not expecting the cultural differences. Depending on the anime, there can be a lot that you just don't get - although the more you watch, the more you get those idioms thanks to past exposure.
The anime I'd recommend, for American viewers at least, that make it easier to get into and to see how brilliant the genre can be, include:
Eve no Jikan (Time of Eve) - a six-episode SF series
released for free on the web. (Subtitled, but well worth the effort.) Includes Asimov's 3 laws of robotics, but in a story that makes better use of them than Asimov ever did.
Ghost in the Shell: Stand Alone Complex (both seasons) - great characterization and story in a near-future world where most people are connected directly to the net; focuses on Section 9, a secret, special-forces anti-terrorism unit. Engaging and morally complex; explores existential themes and others that fans of thoughtful SF enjoy. Has great action but is more dialogue-driven and thought-provoking than fans of modern action movies necessarily would have patience for. (I.e., folks with Worf's Lament should skip to the next recommendation.)
Sword Art Online - Also has great characterization and story; it's SF but set mainly in a virtual reality that is a swords-based fantasy context (with minimal magic). Easy to like the characters and the art style. Has its fair share of fighting, too.
Miyazaki movies, especially
Ponyo and
Howl's Moving Castle for their powerful, character-driven stories. Ponyo not only is accessible for a wide audience but is especially good for folks with kids, as it has appeal for both groups, like Pixar films do. Disney recently sponsored fresh DVD / Blu-ray releases of most of the Miyazaki movies in the U.S.; definitely worth getting if you haven't got them already. (Miyazaki is where my list diverges from my main interest area, science fiction, but there's a lot of great anime from other genres out there, too, such as
Death Note,
Full Metal Alchemist: Brotherhood, and the film
Tokyo Godfathers.)
Matthews said:
Perhaps the animations are better today, but the content... isn't.
Off the top of my head:
- Paranoia Agent
- Anything by Studio Ghibli [Miyazaki - yes!]
- Planetes
- Mononoke
I agree with all of these; haven't seen the others yet - though Puella Magi Madoka Magica looks good through first 2 episodes.
Planetes especially for SF fans; the story's not as rich or in depth as something like Ghost in the Shell, but the science is great; people from JAXA, the Japanese space agency, served as consultants on that series, so the physics of space travel and other elements of life in orbit are all very realistic.
Cowboy Bebop, too, which marries space-based SF bounty-hunting (the "cowboy") with musical themes (the "bebop"); pretty cool, and also often funny, though arguably harder to get into than the first few series and films on my list.
I'm surprised no one's mentioned Macross /
Robotech - the series from the '80s that got me into anime in the first place.
Outside of anime, others already have mentioned many of the ones I like. I'd also mention
Phineas and Ferb as a great series for both kids and adults; the art style takes a moment to get used to (the characters have odd-shaped heads), but the writing's phenomenal, and there are lots of SF allusions and other cultural references in the series. Fun stuff!
-m