Over the past few days, I've been playing two games in particular: Mirror's Edge and Borderlands. Here, though, we have two very different ways of avoiding the 'brown problem'.
Let's start with the former. Mirror's Edge makes use of white like most games make use of brown. The buildings, streets, drainage canals, walkways, AC units... virtually everything in the city is pure, eye-burningly stark white, right down to the cardboard boxes and benches and other detritus that you encounter during the course of the game. Obviously, this is as much a device to tell the player they're in a sterile, utopian society as it is a design choice; accents of orange, green, blue, pink, and various other vivid colours are used to draw the player's attention to where they're meant to go, or to detail an area. In places, even the lighting and shade are coloured. This is the all-out, dead-opposite approach to what we're becoming used to, as brown usually represents something dirty or old.
Perhaps the credit for the more interesting of the two approaches, though, goes to Borderlands. While the game itself is largely brown by necessity (Pandora, of course, being one giant wasteland), the player's weapons - the things they will see every second they are playing the game, in the bottom right corner of their screen - are so vividly coloured they put even the Halo series to shame. Kill a lot of enemies in one area, and you will find a veritable rainbow of weapons lying on the dusty ground. The fact that Gearbox found a way to add some colour to a game which takes place on a dustbowl planet is impressive; the fact that they did so without hurting the atmosphere is even more so. If only more developers would try to inject some variety into the sea of brown... as even deserts have colour.