Celshading is a distinctive method of shading that gives the appearance of anime or cartoon. It does this by calculating the incident angle of the light hitting a surface, and putting the light into four different colours: Specular (usually bright white), highlights, midtones, and shadows. Celshading is becoming more and more prevalent in video games and tv and movies. Several popular animes (notably Blood: The Last Vampire, and FuriKuri) make use of computer animation with celshading to give them impression of being handdrawn. One of the first games to make use of celshading was the dreamcast game Jet Grind Radio. It's quite common in Quake 3 where shaders can be baked into models, allowing for an entire legion of anime models and skins to be churned out by the Quake 3 community. Because celshading requires more cycles in the CPU and video card than tradition openGL lighting, models and textures are usually shrunk down to compensate for the lack of speed. In most cases, the edge detection is somewhat flawed, resulting in thick black lines disapearing and reappearing when transparent surfaces overlap. Celshading is not perfect; it would be nearly impossible (and just plain nutty) to try and fix all the problems with it. Similarly, conventional shading has problems too (aliasing, clipping, smoothing seams, etc) but the problems are very minor and superficial in nature so they can be overlooked.
Celshading is becoming quite prevalent, as artists look for an alternative to the ultra realistic approach established for games and computer animation. The XBox would appear to be a perfect machine for celshading as it has dedicated pixel and vertex shaders that can calculate celshading on the fly without it having to be programmed much deeper in the games graphics engine. The celshaded look is only going to appear more, but luckily the novelty hasn't worn off among North American culture. Let's hope it doesn't go the way of the ubiquitous lens flare.
A very good example of celshading contributing to the essential style of a game is the new Legend of Zelda game, previewed at E3 2002. The graphics were well developed and the style and feel of the game is reminiscent of the Super Nintendo days, or even the short lived Legend of Zelda cartoon.