Anime DVDs/Blu-rays in general (at least in Japan) love doing this, with the Limited Edition having limited edition cards, bonus CDs, fancy artboxes, the works. They're also hideously expensive.
Sometimes, CDs normally released separately, like image songs and the soundtracks, are packaged with the DVDs/Blu-ray, giving more incentive to buy them.
Anime merchandise also has this tendency, especially figurines; often an altered figurine gets released at the same or later, but the only noticable difference is the paintjob such as non-standard colours for the hair or clothes, though there are also examples where even the skin colour is different (tanned, for example), or a different facial expression. Usually the super-special version costs the same as the original, thus offering fans a legit choice, but sometimes the special one is only available at conventions or online and then typically much more expensive.
Although it sometimes occurs with later DVDs, the first volume of most anime series gets released as a DVD-only and as a DVD in an artbox designed to hold the entire series.
Collectors editions of Naruto DVD volumes came with action figures of Naruto (both part 1 and Shippuden), Sasuke, Kakashi, Shikamaru, Rock Lee, Neji, Minato, Gaara, Itachi, Deidara, Sasori, Gamabunta, Gamakichi, Tonton, Pakkun, Katsyuu and Manda.
.hack//SIGN did this when it came out on DVD in the US. They had the regular DVDs and then they had the special edition ones with a Soundtrack CD in each. Except the last two. Second to last had a box to put the previous CDs in, and the last had an extra disc with a few special features on it.
They did this with their UK release of Fullmetal Alchemist (2003), with an ultimate edition including a resin replica of the Gate of Truth, an artbook, art cards and even a certificate with the buyer's name and State Alchemist rank, signed by King Bradley. Regular collector's editions come with the art cards.
Their collector's edition of Eden of the East features a translated copy of the log book, art cards and three little stickers, all bundled in a nice envelope.
They've also released a collector's edition of Noragami Aragoto, which comes with art cards and a box to hold both seasons on Blu-ray.
Their Ouran High School Host Club a collector's edition has a nice box, stickers and a "photo album" booklet.
Their Blu-ray collection of Gangsta. comes with a booklet featuring art and the sign language used in the series.
The Ultimate Edition of Terror in Resonance comes with a unique cover for the Blu-ray case, a tray with a sketch of Nine and Twelve on the back, the "Ultimate Artbook", and a very nice box to hold it all in.
The Collector's Edition of Manga/Claymore comes complete with an art book and several art cards.
Their Collector's Edition of Angelic Layer also comes with an art book.
Their Collector's Editions of Literature/Durarara x2 come with extras; for Shou, there's a booklet and stickers, and for Ten and Ketsu there are booklets and art cards.
For Manga/Kokkoku, they bundled their Collector's Edition with art cards and a poster.
Their first-print run of the first part of March Comes in Like a Lion came with a poster as a pre-order bonus; both parts come with booklets.
Their ultimate edition release of B: The Beginning comes with an A4-sized art book, art cards, and the OST on CD.
Likewise, their release of Bartender includes four drinks coasters and nine cocktail recipe cards.
For their release of Black Lagoon, a booklet and poster are included.
Their release of Manga/Kakegurui comes with a booklet and four large playing cards with images of four of the main ladies.
They released the first season of the anime adaptation of The Heroic Legend of Arslan, which comes with a booklet of character art and a very nice embossed box.
Their releases of Violet Evergarden and the movies are well-stockd with extras, ranging from sticker books and character guides to copies of letters written in the series.
Aniplex USA is one distributor that became well-known for their premium releases. Some fans dread them due to their high prices, while others are happy to have such high-quality releases for shows they really enjoy. Some examples:
Kill la Kill was released over five volumes, each of which had a $75 retail limited edition release. These sets featured posters, postcards, one video/audio extra each that wasn't included on the regular edition (such as making-of documentaries, soundtracks, and cast interviews), and collectible PR cards.
Tengen Toppa Gurren Lagann received an imported 15-disc set, which included every episode (including audio commentary for some), the movies, an OVA, music video, cast interviews, drama CDs, a documentary on the making of the Childhood's End film, a hardcover book of production materials/art for the series, and an exclusive new design for the box set. This set came at a $670 retail price.
Sentai Filmworks released Beyond the Boundary with a plethora of extras, including a pair of Mirai's glasses, a rubber keychain of Mirai, art cards, a lanyard, a poster and a booklet. Averted in the UK, where there was just a regular Blu-ray/DVD release. However, the UK release of the movies came with a poster and art cards.
In Japan, the limited editions DVD/Blu-Ray releases of the A Certain Magical Index anime and its spin-offs include a mini-novel written by the series creator, with the entire set being the equivalent of one or two light novel volumes. The focal characters of the novels depend on the anime in question.
For Railgun, the include novels focus on a specific member of the magical community.
For Accelerator, its lone novel has a prequel story featuring the main protagonist of Index.
With the US release of Code Geass, Bandai planned out three different releases, specifically targeting the different levels of anime fans. For casual fans, there's the Vanilla Edition single DVDs and "volume packs" (two DVDs packaged together). For the real fanatics, there's the Limited Special Collector's Ultimate Edition, which is a two-pack plus a Sound Episode CD, an official soundtrack CD and a volume of the spinoff manga.
Bandai's release of Ghost in the Shell: Stand Alone Complex was handled quite beautifully. On top of the vanilla editions for all 14 DVDs (covering both seasons,) a special edition was released as well, and it only cost about $10 more. The 14 DVDs provided 2 figurines of Motoko, 1 of Batou, 1 of Togusa, 2 Jameson units, 3 Tachikomas, 2 Android Maids, a 2nd Gig mousepad, a Laughing Man t-shirt, the first three Original Sound Tracks, a Section 9 Employee badge, as well as Tin DVD cases to hold the DVDs in. Also, the 2nd Gig DVDs themselves came in metal cases, which themselves are stored in a rather fancy tin DVD case.
When Ginga: Nagareboshi Gin was released in certain European countries in the 80's, it went through several cuts due to censorship and attempts to fit the series on four VHS tapes. Eventually over 100 minutes of the original material was left out from this release, causing the dubbing to be least of the worries. Later, when Finland and Sweden received uncut DVD releases with original soundtrack and voice acting intact, it was marketed as Special Edition of the series.
Nagareboshi Gin's sequel, Ginga Densetsu Weed, got a Collector's Edition box set release in Finland and Sweden, too. In addition to including the entire series it also comes with a Weed phone strap and a leaflet with extra information on the characters.
This was also done with the US release of Lucky Star (except for the last volume). Turned out it was almost a money black hole for the producer.
Likewise with Puella Magi Madoka Magica. Aniplex released the series across three DVDs, which is quite normal. The vanilla editions cost your usual $30 or so, depending on where you buy it. Then there is the Limited Edition for all three DVDs which comes with artbooks, stickers, three soundtrack CDs.. all for the cost of $90. Each.
The Italian/German Limited Editions are similar to the US ones, except cheaper (50€ each, something like $55), and with slightly different extras (The boxes included both the DVD and Blu-Ray releases, and instead of the stickers thay had Nendoroid Petites of Madoka, Mami and Homura)
Aniplex also handled the DVD release of Durarara!!. While the DVDs are split up into your now-standard "Part 1 and Part 2" sets, both of them cost about $70, and there are no special editions.
Hellsing Ultimate does this with multiple releases, there's the single disc version, with just the OVA, there's the Two-Disc Version with commentary and a special features disc, there's also the Two-Disc Steelbox which comes has the two discs in a nice steelbox case, and sometimes comes with an artbook. You can still find the Steelboxes for a decent price brand new, but all the other editions are just as expensive.
Each season set of Inuyasha came in two versions (at least in America): One was simply the discs of that season in one set. The collector's editions came with show related memorabilia such as the Beads of Subjugation (Season 1), hanko signature blocks (2), Kagome's jewel shards (3), Miroku's prayer beads (4), Sesshomaru's scroll (5), Collector's watch (6) and an Inuyasha figure with Adamant Tetsusaiga (7).
The limited edition of Legend of the Galactic Heroes in North America has a retail price of $800, and is limited to 1,000 copies. It includes the complete 110-episode OVA series, the 52-episode Gaiden series, all three movies, a hardcover book, commemorative metal coins, 3D lenticular visual cards, and a nice box to keep it all in.
The only way to watch the uncut version of Mach Go Go Go or its 1997 revival with English subtitles in the US is the Speed Racer Collector's Edition, which also includes the classic English dub in a case shaped like Speed's head.
Manga Entertainment have done this with some of their more popular titles, such as Dragon Ball Z: Battle of Gods and Attack on Titan. This move was actually criticized by some fans and reviewers because it involved taking extras off of the existing US versions (from which the UK releases were based), and in the case of blu-rays downgrading the extras to DVDs to boot.
Manga UK have released several Kazé titles in the UK in this fashion; Tiger & Bunny, Princess Jellyfish and One-Punch Man, all of which came with extras. For Tiger & Bunny, there are little magazines that follow the plot of each boxset part as well as two Hero Cards per boxset; for Kuragehime, they included a plush keyring of Clara as well as a nice box to hold the DVD s and the keyring in; for One-Punch Man there's a booklet containing character notes and staff interviews; it again comes with a nice box.
MVM Entertainment released a Limited Edition of Monthly Girls' Nozaki-kun that comes with the Blu-ray and DVD, as well as a third disc with the OST on it, all in a very nice box.
The limited edition of Shimoneta comes with an exclusive box set that contains a sticker, two pins, and a tube sock (which makes sense if you're familiar with the nature of the show).
The mass-market Collector's Edition which includes the ADV 1997 English dub and the Japanese subtitle translations commissioned for that release of the series, Evangelion: Death (True)2 and The End of Evangelion, as well as art cards and a condensed version of a companion book.
The 5,000 copy per region Ultimate Edition, which also includes full-size art boards from the original Japanese Laserdisc releases, the ADV dub, a resin paperweight of Sachiel, the full version of the companion book, and a NERV ID card with lanyard.
released a Limited Edition of Monthly Girls' Nozaki-kun that comes with the Blu-ray and DVD, as well as a third disc with the OST on it, all in a very nice box.