After writing a quick script to go through BrickLink inventories:
davee123 wrote:LEGO didn't really start using [Old Brown] very much in sets until roughly 1999ish.
Looks like for its early life, Old Brown was mostly used in things like minifig hair, brooms, treasure chests, and so forth. Not really "standard" elements. It first started getting used in more building elements in 1986, but only rarely. For instance, a 1x2 brick and 1x2 plate were used with brown horses (sometimes a 1x2 tile instead of a plate).
In 1993, Dragon Masters used more standard elements in brown (still not very much) for a few trees and natural landscape. Mostly a small blip on the radar, and Brown was still very much a fringe color.
In 1996, mostly with Wild West and Dark Forest, Old Brown started being more common. Probably sort of the same way we might view Dark Brown or Dark Tan today-- not very plentiful, but in existence.
Then, in 2000, brown's usage took off, and kept increasing through 2003, when it was discontinued.
Reddish Brown, starting in 2004, took over where Old Brown left off (as a common color), and has since increased in use. A lot of that increase in usage may be due to the fact that more sets are released these days than they were historically-- but regardless, Reddish Brown is now a pretty common color.