Oi! started pretty much in the latter part of '77 as a reaction to the more arty turn punk had been taking at the time. It was an attempt to bring punk back to the subject matter that affected working-class street kids' day-to-day life, and musically it was based on early punk bands such as the Clash and the Ramones mixed with early british rock like the Stones and the Who. The bands were often comprised of punks and skinheads, and the music was always a favorite of skins'. At the time the term Oi! didn't exist as a musical description, and this particular style of punk was called "Street-punk" or "reality-punk". The original oi bands included Cock Sparrer, the Cockney Rejects, Angelic Upstarts, Slaughter and the Dogs, Skrewdriver, the Lurkers and the most well-known was probably Sham 69.
Unfortunately, during this time many (but not all!) skinheads had been recruited by right-wing, racist organizations such as the National Front, and the music began to be associated with racism in the minds of many people, which is an unfortunate myth that continues to the present day, with many mainstream histories of rock dismissing all oi as being racist music. None of the original streetpunk bands were racist or espoused right-wing politics with the exception of Skrewdriver, although they didn't make their views public until the early 80's. (Their early material is considered to be classic oi by most).
Anyway, by the early '80s there was a whole new movement built around the streetpunk sound with the most well-known oi! bands, including the Business, the Last Resort, the 4Skins, Combat 84, Infa-Riot etc. This movement was labelled "Oi!" by music journalist Gary Bushell, and the movement was seen as promoting unity between punks and skinheads. There was also, at this time, a small neo-nazi rock scene emerging headed by Skrewdriver, and the music these bands made was basically the same as Oi, but the bands sought to distance themselves from punk in general, preferring the term "R.A.C." (rock against communism). These bands really had nothing to do with the oi scene besides a similarity in musical style and the fact that they were supposedly "skinheads" (most skinheads i know would beg to differ).
Anyway, the oi movement started to lose momentum in the U.K. by the mid-'80s, but at that time healthy oi scenes were developping all over Europe, North America and even in Japan. For some reason in the mid-'90s there has been a huge revival of interest in oi music, with literally hundreds of new bands emerging, and bands that had been around for years finally getting the recognition they deserve. There is a much more concerted effort nowadays to dissassociate racism from oi in the minds of the public, and today all of the bands recognized as being part of the current oi scene are openly anti-racist. (Meanwhile, nazi music has turned away from oi and towards really bad heavy metal). Some of the better oi bands today would include the Templars, the Wretched Ones, Those Unknown, the Lager Lads and Oxymoron.