Disney Anime Company
A bit of info about Disney.
Walt Disney Studios Home Entertainment is the division of the vast US-based Disney media empire that handles distribution of DVDs and Blu-ray for the home video market. While the division was created in the early days of VHS to handle Disney's century-long catalog of homegrown animation, and that's still their main purpose, in the mid-'00s they signed an exclusive license to distribute the films of Miyazaki's Studio Ghibli in the North American market. Given the oft-made analogy of Miyazaki as Japan's Walt Disney, the match seems appropriate, and indeed it has resulted in a catalog of fine releases even from the perspective of a discerning anime fan.
Miramax is a separate entity also owned by Disney, which has handled the release of more mature Ghibli titles, such as Princess Mononoke.
Though non-Disney films only make up a small part of their catalog, they have almost the entirety of Studio Ghibli's catalog under license. This includes some of the most famous and beloved anime films of all time, including Nausicaa, My Neighbor Totoro (originally distributed, dubbed only, by Fox), Kiki's Delivery Service, and Laputa, to name a few.
Other Disney divisions have released a few of Ghibli's films targeted at more mature audiences; art-house distributor Miramax, for example, has their name on Princess Mononoke.
What Their Releases Are Like
Disney doesn't exactly have a great reputation when it comes to leaving well enough alone, but in part because of Ghibli's insistance on doing things right, and perhaps in part because of Pixar's involvement (Pixar head John Lasseter has some introductory comments before the film on many of their DVDs), almost all of their releases have been stellar.
Every new Ghibli film gets a fairly high-profile theatrical release, followed by a DVD and Blu=ray release.
Their first wave of Ghibli back-catalog DVD releases were completely uncut, included well-written English dubs with some very high profile actors, full Japanese audio and accurate subtitles, and often dubs in one or more other languages as well. The production values are, unsurprisingly, of the highest calibre, and they usually include a number of special features as well--often an entire second disc full, including storyboards. Miramax's Princess Mononoke DVD was of almost the same quality as the main-label releases, though with less extras.
Some of their later (2010-era) re-releases haven't been quite as stellar, including dubtitles instead of a more accurate translation, though they are still solid and well-produced.
In an interesting twist on the tendency to re-record the music for a dubbed release, Disney actually brought original composer Joe Hisaishi in to add additional music to the soundtrack for the dubbed release of Laputa (also expanding the synthesizer work with a larger orchestra).
In addition to releasing new films on Blu-ray, they've also begun working their way through their back catalog, including at least one film--Whisper of the Heart--which I would have expected to be the last to get the high-def treatment. Their BD releases have the same attention to detail as their other releases, and also kick in a DVD of the movie, for good measure. Disney, known for anti-piracy paranoia, has been slow to adopt online distribution.