Remaster

"Each print has been completely restored, digitally remastered, restored again, then reverted back to crumbling nitrate film stock just for the jolly hell of it."

- Jeff Fitzgerald, "Rare Jazz Films Restored"

Taken in the literal (and original) definiton, "remastering" is a process where video and audio is edited to (in theory) look newer, brighter, cleaner, etc. and put on new Master Recordings, likely of the digital kind in the post-90's world. It initially started with music in the move to CD Audio, and lately is more associated with aged movies.

Literal definition aside, though, Remastering is associated with the process of making an old product look more modern, or at least like it's in mint condition. The usual process of a remastering includes suchs things as;
 * Making the product look more colorful (Messing this up may lead to more brown, or oversaturated colors)
 * Making the audio sound more clear (although some just make stuff louder)
 * In the era of hi-definition, increasing the resolution of the masters.
 * And of course, some companies may think "Remaster" is a metaphor for "any kind of rerelease we feel like doing", and do changes to the product outright.

This normally does not happen to videogames because they're already digital (and thus, every copy identical to the original) by nature - they would be more prone to get an Updated Rerelease or a Video Game Remake instead. Since the process tends to imply making an old product look like it's new, it can be seen as the opposite of a Retraux.

The quality of a remastered product tends to vary a lot. Generally, though, people appreciate Remasters the best when they're able to increase the visual and audio quality of their product/make them enjoyable to watch on their new Hi-Def monitors with as little modifications to the source material or their memories of the product as possible. Digital Destruction and Loudness War are when the Remaster actually makes the product worse than before; unfortunately, the common consumer is typically unaware of this happening.

Remastered products tend to be sold as a Special Edition or an Anniversary Edition.

The Other Wiki has some more general information. Also look up Master Recording for information on what Masters are when referring to this - so as not to confuse it all the other kinds of masters there are or are not.

Anime & Manga

 * The Dragon Box Sets. Most certainly not FUNimation's previous Dragon Ball Z Box Sets.
 * Neon Genesis Evangelion 10th Anniversary Collection. Painstaking efforts to eliminate as much grain as possible while keeping in as many details as possible were made, as well as fixing the infamous "shaking-camera" effect that the original footage suffered from. It's almost impossible to see any grain in the new footage at times.
 * Typically, anime from the 80's and early 90's get a clean-up job, with visuals made more contrasting in color and audio made crisper, when DVD/Blu-Ray releases come around. In most cases, the fans like them.
 * Lately anime from the 1960's and 70's has been getting this treatment as well, although most of it so far is a case of No Export for You or such.
 * Revolutionary Girl Utena has a rather notable remaster in that the grain reduction wasn't the biggest goal for them. In order to keep the fine lines and details in animation the show was famous for, they focused on color correction and redoing most of the sound effects. This has resulted in one of the best remasters of 90s anime, according for some reviewers, stating that it is on the same level as the Neon Genesis Evangelion 10th anniversary collection mentioned above.

Films -- Live Action

 * Star Wars has had multiples of these IIRC, starting with the Special Editions.
 * To Kill a Mockingbird uses many zooms in the film by zooming in the negative, increasing grain size. Instead of removing the grain for Blu-Ray, the restoration team matched it with the other grain to make the effect more seamless, while keeping the original picture.
 * Monochrome/Black and White movies. Sometimes companies try to color them, too, but that tends to upset some people.
 * Some DVD bonus features of films directed by The Coen Brothers parody this with Forever Young Film Preservation, whose "accomplishments" include restoring The Grand Lebowski (sic) using an Italian film reel and redubbed audio, and making Blood Simple more "worthy of preservation" by cutting out "the boring parts".

Live Action TV

 * ABC advertised a Remaster of Mighty Morphin Power Rangers, with CG edits, increased color saturation, higher contrast, a bit less print damage than some recent airings.
 * Again, black and white television.
 * The team that remaster the classic Doctor Who episodes care so much about the series that they practically (and sometimes literally) invented several methods of remastering (such as RSC, VIDFIRE, and the colour recovery techniques).

Music

 * Pretty much anything transferred from pre-CD tapes to, well, CD tapes or some other Digital media.
 * Many, many acts have remastered (and even remixed) part or all of their back catalogue long after the original mixes were released on CD. This isn't always a good thing.

Video Games

 * Strangely, Don Bluth Studios made remasters of Dragon's Lair and Space Ace - even though the arcade games were already digital to begin with - for Hi-Def action. This makes these a notable case of video games being remastered.
 * Well, laserdisc video's actually analog.
 * Kinda questionable if it counts (yet), but with the way Satellaview games were released as ROMs - with huge chunks of data missing and all - many of the games require extensive hacking to make a project out of which requires restoration of variuos missing contents. Just check out the BS Zelda hacks, and compare them to the "original" ROM dumps. The difference is almost as drastic as the difference between a prototype and a final game. This trope applies more to the Satellaview's Soundlink audio, but so far the scale isn't quite that high - only a select few songs have been attempted so far, nothing amounting to the amount required for a full game.

Western Animation

 * The Golden Age of Animation tends to have various cases of remasters with large amounts of controversy and drama.