Anime Takeout is probably the best US site for anime (Japanese animation) and manga (graphic novels), with a very slick site to boot. This delivery of manga is added bonus--acting just like one of your DVD slots.
Anime Takeout lists only 12 genres (your typical ones, Drama, Romance, Fantasy, etc) instead of getting creative and breaking them down further into categories that would suit anime better. But that's a minor criticism. They do have browsing via user rating (rare and very useful), and by maturity rating, and by series (with many dozens listed).
The actual data for each title is good, with a very large box cover picture, a summary, then details like running time, release date, rating, studio, aspect, audio, and subtitles. Some of the reviews we read were very compelling--clearly written by anime enthusiasts with a good background in the genre, and would definitely affect whether or not I'd rent a given title.
We especially like their Availability Meter, which gives you a rough idea of how many people ahead of you are waiting for a particular DVD. This will give you a rough sense for how long you may have to wait. Of course, by putting the DVDs you want the most on top of your queue, you maximize your chances of getting something sooner.
While they do stock manga, they do not currently stock hentai. Manga is shipped via US Postal Service First Class Media Mail. You can rent them just as you would an anime DVD; each book takes up one slot. You do need to report if the copy is damaged though, as they evaluate the quality of the books; needless to say, you don't want to damage them.
Anime Takeout notes it will typically take 2-4 days for DVDs to arrive, though we believe this will depend heavily on your proximity to the West Coast. They ship to all 50 states, and if you email them, they can set up something for US military personnel stationed overseas.
To aid speeding things up, they have an excellent Self Return function; just log in and click that you've sent your discs back, and Anime Takeout will send you the next lot without waiting for the first lot to arrive.
Reports on the web of Anime Takeout's service indicate broad satisfaction; they certainly have a strong loyalty base, with people willing to pay that bit more for this very specialized service. One person raved that he had never received a scratched disc out of 200 he'd rented from them, no doubt because of the delicate foam sleeves they use.
Prices: Anime Takeout do not have a free trial, but they do offer two subscription offers (there used to be seven, and much cheaper than they are now unfortunately). They offer unlimited tariffs for two discs out for $25.95, and four discs for $41.95.