As far as easily enjoyable goes, though, I would most definately recommend Moribito/Seirei no Moribito. An English dub only exists for the first 10 episodes (which were very well performed). Aparently, Adult Swim cut production after the first 10 episodes for no apparent reason. That said, you'd have to watch the rest in Japanese. The sub-work is good, though, so not too many details should be "lost in translation." I've never seen a better rendered series, either. The visuals are truly superb.
Actually, your info is a bit out-of-date and/or incorrect. Moribito was originally licensed by Geneon Entertainment, who commissioned its dub. (Just to clarify, [adult swim] doesn't produce the dubs for any of the series that it airs; it merely obtains broadcast rights from the American licensors.) When Geneon ceased in-house distribution of titles and lost many of their licenses, the licensor Media Blasters took over the distribution rights from them. (Media Blasters has been mostly dealing in more niche series released sub-only lately, so they presumably got a good deal on it.) [adult swim]'s deal to air the show was originally made with Geneon, so when they all but closed, the broadcast rights presumably reverted to their Japanese parent company; the head of Media Blasters confirmed that his company never held the TV rights. [as] originally broadcast only the first ten episodes of the series at the ungodly hour of 5:30 AM because that was all they had to show; apparently, there was some delay in getting the video masters from Geneon to Media Blasters. [as] later re-aired the first ten episodes at a more reasonable timeslot, but due to the whole licensing snafu, they were forced to stop airing the show, and it looked as though they might have to give up the rights entirely.
But to get to the point of this whole convoluted situation, [as] recently started re-airing the series from the beginning for the third time, and they're going to continue past the tenth episode and run through the entire series. It's currently in the 1AM slot on Saturday nights (or Sunday mornings), and I think this upcoming Saturday's episode is the eighth one. All of that stuff aside, I completely agree with the recommendation; Moribito is an utter gem of a series that seems to have flown under a lot of people's radar.
And just to throw in one last remark to TrashMan, FLCL's creators have discussed/confirmed essentially everything that Flaser mentioned, so there's no "are or aren't" going on there in the least.

In deference to our esteemed mod, I won't say any more, lest I raise the wrath of his drunk-fu.