Most Japanese anime tends to be... well, stupid, quite frankly. If it doesn't involve giant fighting mecha-robots transforming into the most unlikely of shapes (e.g. RoboTech and pretty much EVERY GUNDAM SHOW EVER), it will involve a harem of hilariously well-proportioned girls running after one highly inept and/or perverted guy (e.g. Rosario + Vampire, Heaven's Lost Property, Demon King Daimao).
The few happy exceptions to these rules are genuinely interesting, fun, and imaginative- Ah! My Goddess is of course the standard-setter for this type of anime, and Arpeggio of Blue Steel is also a good example of a show that is both visually impressive and thought-provoking. However, most of them still revolve around quite odd situations and fantastical events.
There is one good show, though, that doesn't involve most of the standard anime tropes. It's a highly underrated show called Spice and Wolf, which is currently available via Hulu or YouTube (via a paywall, annoyingly).
The show's premise is quite intriguing. Set in a Mediaeval-ish, European-ish environment, it focuses on a trader named Kraft Lawrence who is attempting to make his way in the world and profit through trade between various city-states. On his journeys, he meets the wolf-goddess Holo, who enters into a bargain with him: in exchange for her help in his ventures, he will take her back to her ancient home, the mythical land of Yoitsu.
Yeah, I know, it sounds stupid. But it's done really rather well. The anime itself is based around an ongoing Japanese light novel series; the anime episodes stopped at around the end of the third volume, and as far as I know there are no plans at present to do any more.
Unusually for an anime, this one focuses on trade and personal relationships, instead of swords/sorcery/demons/cosmic accidents/blowing stuff up. It is, in many ways, a highly refreshing change from the often dreary and repetitive (not to mention silly) escapism of most anime shows.
Here is probably my favourite episode from the show- unfortunately, whoever ripped this version did an absolutely terrible job with setting the playback speed, because everyone sounds like a chipmunk: