Truer to the Text

If a book or comic becomes sufficiently popular, it will almost definitely get a TV show or a movie. While some fans rejoice upon hearing that their favorite series is getting an adaptation, all too often the hardcore fans will find themselves bitterly disappointed, and problems are especially likely to surface when the story is ongoing and the staff has to work with incomplete source material. The result of such circumstances tends to be a Base Breaker.

Sometimes, these complaints are heard, and the result is a Truer to the Text adaptation. When this happens, the story gets another adaptation, or at least go out of their way to cover what they missed out on last time. This time there will be no annoying additions, no alternate ending, no important details ignored, just the original story, pure and proper. If done well, the Fandom will probably be quite pleased.

However, it's important to keep in mind that this is not necessarily a good thing. There are four closely related problems with this sort of adaptation.
 * The first is that, however divergent, a series' first adaptation will probably at least begin with the same basic plot, which could give it a repetitious feel; the reboot starts by covering ground that's already thoroughly trodden.
 * Thus the second problem: the beginning might have to deviate from the original story to make a re-adapted story seem new.
 * Thirdly, not all fans of the movie/show actually read the source material. This means that they have no idea what they're supposed to be waiting for, so it might feel like this second version is just more of the same.
 * Finally, depending on the differences between mediums, such as the inevitable problems that come with adapting a book into a film, "more faithful" does not necessarily equate to "better".

Compare Mythology Gag.

Adapted from Comics

 * Arguably, the purpose of the Marvel Cinematic Universe. It's run by Marvel Studios, rather than owned by an independent studio (such as Fox, Sony or Universal), so they have direct control over the movie they put out. The Incredible Hulk and Captain America: The First Avenger are significantly more faithful to the source material than Ang Lee's Hulk or Captain America (1990 film) were.
 * Tim Burton's Batman was this to the Adam West series, being darker and moodier. After it suffered Adaptation Decay and became Lighter and Softer Christopher Nolan's The Dark Knight Saga became this in it's own right.
 * This is debatable. At the time, the Adam West series was incredibly faithful to its source comics, and the Burton films were way darker than most of the comics at the time, tweaked Batman's origin story and the Joker's past, and showed Batman acting out of character in regards to killing.
 * The Amazing Spider-Man is a little more faithful to the comics than the previous movies. Peter's in high school, Gwen's his first girlfriend, he has mechanical web shooters, his parents have a mysterious past, he's a joker, etc.

Adapted from Literature

 * Bram Stokers Dracula and Mary Shelley's Frankenstein were intended as faithful adaptations of two books that had been quite heavily changed in previous film adaptations. They had their own changes and quirks, though.
 * The 2000 Dune miniseries took some liberties with Frank Herbert's book, but compared to the 1984 David Lynch movie, its fidelity is nigh-slavish.
 * The 1997 miniseries of The Shining was far closer to Stephen King's book . This is a strong example of "more faithful" not equaling "better": the miniseries was underrated (and scarily effective in its own right), and the 1980 film has significant weaknesses, but Kubrick's vision—however un-Kinglike—still resulted in a better movie.
 * The Coen Brothers said this was their intention when they made their film adaptation of True Grit.
 * Carson McCullers adapted her novel The Member of the Wedding for the stage herself, despite never having written a play before, to preempt the production of a more conventionally theatrical adaptation by another writer.
 * The first two Harry Potter films are noticeably closer to the text than the movies the followed. On the Sliding Scale of Adaptation Modification, the first two movies would score a "4" and the rest would score a "3". Fans are divided over which approach was better. Critics are less divided and prefer the later films (except for Roger Ebert).
 * John Carpenter's The Thing compared to A Thing From Another World. The older film used the beginning of the plot of them finding UFO in the ice and it containing and alien, but from there diverged quite a bit. Carpenter's version had the alien keep it's assimilation powers and overall stayed much closer to the plot of the book.

Adapted from Manga

 * Fullmetal Alchemist: Brotherhood was to be a far more faithful retelling of the Fullmetal Alchemist manga. The anime adaptation, in this case, was quite popular in its own right, but at the same time, it left fans of the manga livid. That said, many fans found Brotherhood lacking as well.
 * Hellsing, in a rather similar vein, got a more faithful adaptation in the form of an OVA series, titled Hellsing Ultimate.
 * Mahou Sensei Negima is an interesting case. The recent OVA releases have been faithful to the manga, but they're so deep into a story that none of its multiple previous adaptations properly covered, that they won't make much sense to anyone who hasn't read the manga.
 * A new anime for Hunter X Hunter has been announced for the Fall 2011 Anime season, to be a retelling from the beginning. Whether or not this turns out to be a "truer" adaptation has yet to be seen.
 * Dragon Ball Kai serves as a remastered Adaptation Distillation of the first Dragonball Z anime, with most of the Filler removed (not to mention greatly reducing the original show's infamous abuse of Talking Is a Free Action).

Adapted from Visual Novels

 * The anime version of Tsukihime left many fans quite bitter over how much it deviated from the source material. Correction, there was no Tsukihime anime. There was, however, a manga that retold the original story quite faithfully.