Essential anime, eh? Phew. That's a loaded question.
I also feel awkward posting suggestions for anime on a Christian gaming forum--not because I feel convicted after having watched certain series, but because certain series are not suitable for children or "young" Christians. Several series present ideas popular in Eastern religion and some use symbols from Western religions to illustrate their themes.
Yes, I'm thinking of
Neon Genesis Evangelion.
Love Evangelion or hate it, few people will deny that it's one of the few "necessary reading" staples of the last two decades of anime.
If you decide to watch Evangelion, take my word of advice: DO NOT watch
End of Evangelion, for the love of all that is holy. It took me years to recover. *shudders*
If you want a more lighthearted mecha anime (minus the amazingly messed-up relationships and Jungian philosophy of Evangelion), check out
Nadesico--but skip the follow-up movie,
Prince of Darkness. (Seriously, what is it with writers messing up a decent series with a sucktacular follow-up movie?)
I would back Neirai's recommendation of
Bleach, but for fewer episodes. I feel the story started to drag after episode 20 or so. I haven't started reading the Bleach manga yet, but I got bored with the series around episode 155 and plan to start in on the manga soon.
Shakugan No Shana (both the first and second series),
Noein, and
Dennou Coil are all personal favorites, but I don't know if I could list any of them as "essential" anime. Then again, if Dennou Coil gets set in front of the right Western critics, it could become wildly popular among US anime fans.
You may want to watch a few episodes of
Naruto, just to see what all the fuss is about. After that, drop the anime and read the manga.
For a fresh twist on the vampire mythos, check out
Karin. I wouldn't say it's essential, but it features one of the best (and, ironically, most believable) romances in recent memory.
Like it or not, the Magical Girl genre is integral to the anime education. Skip the
Sailor Moon and go straight to
Mai HiME, which is one of my and my wife's favorite series. You'll get the transformation sequence and dual life motif that are an important part of so many series without the effeminate men. The series is solid throughout, but it
really shines after episode 13.
Another "like it or not":
Akira. It's hyper-violent, the pacing is odd, and it can be terribly confusing, but it was many people's first anime film. Consider this
The Godfather of anime: It's super-violent, so I can't recommend it to anyone, but it's also an important part of the history of the medium.
And don't let anyone talk you into watching
Utena. I don't care how popular the series was. The first four episodes were so repetitive and awful that I couldn't stand to watch any more.
Skip
Hellsing. Terribly overrated and cliche, from what little I could stomach to watch. When I make fun of action anime series that substitute copious amounts of gore for a decent plot, this series is what I have in mind.
You should probably watch a few episodes of the original
Dragonball (not Z, not GT) series--but you don't have to like it. You just have to watch it.
I've read that
Love Hina is the essential harem anime, but that's still not enough to convince me to watch it. The harem genre tends to be predictable and riddled with fanservice, so you could probably skip anything in this field without missing too much.
Outlaw Star was fairly popular in the US, but Cowboy Bebop is better. Way better.
Samurai Champloo is, IMHO, one of the greatest series ever. It has a few violent scenes, but nothing you wouldn't see in 10 minutes of Naruto or Bleach.
Skip
Ninja Scroll. I don't care how popular the movie was. It's way too violent and shouldn't be viewed by anyone under the age of 140.
Nodame Cantible is one of the best series in recent memory. My wife assures me that the manga is just as good, if not better.
Lucky Star is my favorite "slice of life" comedy and was hugely popular among anime fans. Watch it after you've watched a few anime series so you can understand the humor better.
Speaking of humor,
Excel Saga is probably the most popular parody series ever. Again, watch it after you have some experience with anime--and DO NOT watch episode 26. Seriously. Just...don't. Trust me. *shudders*
Suzumiya Haruhi no Yuuutsu is another fan favorite. You'll probably stumble upon a video or animated .GIF of the dance sequence featured in the opening a few minutes into any casual online research on anime.
There are a lot of genres you'll want to avoid. I already mentioned the harem genre; of course, you'll want to skip hentai (which includes several subgenres), ecchi, lolicon, yaoi (gay), and yuri (lesbian) as well.
Remember that even some of the best series have fan service. Don't let that detract from the experience. For example:
Read or Die TV, one of my favorite series of all time, features brief (but not gratuitous) nudity in one episode out of 26. The series is clearly aimed at a more mature audience, so the brief nudity--while unnecessary--isn't contrary to the tone of the series.
Oh, and just in case anyone was wondering, Kusanagi doesn't get naked in
Ghost in the Shell: Stand Alone Complex, so I'd recommend that series, too. Essential cyberpunk.
Man, I could go on and on, but I listed my top three favorites (Mai HiME, Read or Die TV, and Samurai Champloo) and covered several other genres. I'll post again if I think of more, but for now, I think I need to take a break.