Basic Role Playing, or BRP, is the name of the "generic" form of the fantasy-oriented RuneQuest role-playing game rules. A percentile skill-based system, BRP was used as the basis for most of the games published by Chaosium, including Call of Cthulhu, Elfquest, Stormbringer, Elric, Hawkmoon, Superworld, Nephilim, and Ringworld. Pendragon, while related, has sufficiently different mechanics that it can only be seen as a separate system.
At least one non-Chaosium game has used BRP for its core rules. Other Suns, published by Fantasy Games Unlimited (FGU), used them under license. In addition, Corum, a supplement to the Elric! and Stormbringer rules, was published in the fall of 2001 by Darcsyde Productions. BRP was used (without licence?) as the base for the highly succesful Swedish game Drakar & Demoner from Target Games.
BRP was conceived of as being a sort of genre-generic engine around which any sort of RPG could be played, much like GURPS and the D20 system have become today. In order to underscore this, Chaosium produced the Worlds of Wonder supplement, which contained the generic rules and several specific applications of those rules to given genres. Superworld, specifically, began as a portion of the Worlds of Wonder product.
Although similar in a general way to GURPS, BRP is also quite different. Each incarnation of the BRP rules has changed or added to the core ideas and mechanics, resulting in generally compatible games that also provide a slightly different tone or feel to them, or which have slightly different rules interpretations. For example, in Call of Cthulhu, skills may never be over 100%, while in Elric! skills in excess of 100% are encouraged for those who follow Law. Other obvious differences lie in the mechanics -- while both GURPS and BRP are skill-based RPGs, GURPS uses a bell-curve distribution by resolving things with 3d6, whereas BRP uses d100. Also GURPS is a points-based game, much like Champions, where characters are built out of a pool of points, while BRP characters are generally (at least partially) rolled randomly. The degree of random generation varies from specific BRP-based game to game.
I believe the core rules were originally written by Steve Perrin, but I suspect that Greg Stafford, Sandy Petersen, Lynn Willis, and undoubtedly many others contributed to their final form.
Many of the BRP-based games are no longer in print in November of 2001. Currently available systems include Call of Cthulhu and Stormbringer from Chaosium, and the distantly related Pendragon, now published by Green Knight Publishing.
Finally, some note that the 3rd Edition of Dungeons & Dragons, released in the fall of 2000, resembles nothing so much as a reworking -- or perhaps melding -- of Dungeons & Dragons with the rules of RuneQuest (the first BRP-based game), which was first published in 1978. Dividing percentages by 5 and rounding to the nearest whole number results in values ranging from 1 to 20.