Good Stand Alone Anime Movies:
These do not require any previous knowledge of a TV series or OVA to enjoy.
Anything by the late Satoshi Kon
Paprika
Tokyo Godfathers
Perfect Blue, Psychological Thriller (Darren Aronofski's Favorite Movie, and the inspiration for Black Swan!)
Sometime Surreal, Always Poignant.
Fluid Animation met with fascinating narratives about modern life.
Tezuka's Metropolis
Based off the Fritz Lang movie of the same name, it was made after the death Tezuka.
While several of his contemporaries have gone on record saying that he would have hated it, it's still a decent movie.
Ghost in the Shell and Ghost in the Shell: Innocence
See the first one first (obviously).
Best Cyberpunk Action Thriller this side of Johnny Mnemonic
But with writing and philosophical exploration on the same level as Neal Stephenson crossed with Harlan Ellison.
AKIRA
Everyone's recommended this one by now, so why not take the bite?
Wings of the Honneamise
It's an interesting science fiction story backed up with fantastic visuals and overall art design. It's also the most expensive anime ever made, and it shows.
Now some series I recommend:
Nichijou (My ordinary life)
Based off a series of 4 panel gag comics, nichijou is a funny and semi surreal look into the potential absurdities of day to day life. The animation is fantastic, the character designs are crisp, and the comedic timing overcomes any potential culture barriers.
Sayonara Zetsubou Sensei (Goodbye Despair Teacher)
More good animation, matched with an excellent satire of modern day Japan although there's enough similar between our culture that you'll see the connections almost immediately.
It's best black comedy/parody I've seen all year.
Paranoia Agent
More of Satoshi Kon's excellent work, but this time as a full TV series.
Again, semi surreal psychological drama.
flcl (Fooly Cooly)
While we're at it, most Gainax stuff is pretty good. Once you've been versed well enough in Anime fandom, you might want to seek out Otaku no Video, because as interesting as it is you'd need to understand the fandom more to get the parody. FLCL is short and features music by one of the greatest Japanese Rock bands of all time, The Pillows.
Evangelion
With the caveat that you take it seriously coming in, and be prepared to use your brain. It's not a terribly confusing series, as the plot itself requires little understanding of jargon of techno babble, but the characters are very deep and complex as are their motivations and actions. The same goes for the repeated themes and symbolism. It's not confusing, but it is mentally involving and can seem boring or trite if you go into it like an action series or regular drama. Abandon expectation, and just listen to the story that they are trying to tell, or it may be off putting. Seriously, the studio got death threats and graffiti from fans who were outraged over the more cerebral and symbolic ending
Still, the whole series is a standard 26 episodes long, with 1 unnecessary movie, one necessary movie and an OVA remake.
This brings me to an important note:
A note on long running franchises:
Mobile Suit Gundam: 15 TV Series making up 502 episodes. Almost 10 Movies. 7 OVA. 5 alternate timelines and 4 decades of material.
Bleach: 53 Volumes of manga, 358 episodes, ongoing. 4 films and a stage musical.
Detective Conan: 643 Episodes since 1996 and ongoing. 75 Volumes of Manga. 15 Movies.
It's no wonder that some people have a problem getting into anime!
At least Dr. Who stays in just 1 timeline!
If you are going to try to get into a long running or long series, ask around first about where to start. Gundam, for example, has multiple timelines and continuities, not all of which need to be known to understand a given story. So, ask which OVA's and Movies don't really require more than a read of wikipedia.
Detective Conan on the other hand is largely interchangeable. All you need to know can be found in the synopsis on wikipedia. After that, you can just watch any given episode since they're just a bunch of disconnected murder mysteries. Bleach, however, is a bit of slog due to the sheer number of characters as well filler episodes. It can be a real time waster just trying to catch up.
Overall, just keep asking around and watching reviews.
You'll be surprised what you'll find.
