Video Game Music, at the Atari/Nintendo era, usually characterized as people refer to "beeps-boops". In the 16-bit era (Super Nintendo, Sega Genesis), higher sound quality with synthesized instruments. As it progresses, digitized music was born and rest is history.
Video Game Music created a popular cult. Such titles like the Final Fantasy series, Command and Conquer series, Chrono Trigger, Lunar series, Xenogears, are some of the few that people love the music from. Video Game Music is especially popular in Japan, as you can actually buy CD's of the game soundtracks. The popularity of Video Game Music continues to rise, as it begins to expose in America and even the pop scene (especially Faye Wong's Eyes On Me, from the Final Fantasy 8 soundtrack, which the single successfully sell well in Japan).