The wall-bug in DooM is a strange manifestation of the strafe-running speed-up effect that takes this effect to serious extremes. I haven't been able to track down any definitive material on it, and so I can't provide the exact performance statistics, and have absolutely no idea as to why it occurs.
Find a wall that runs along the north-south horizontal axis. This is one that is a vertical line on the DooM map. The wall has to be precisely aligned with this axis; if it shifts a pixel to the east or west along its length, then the bug won't occur at all. This indicates to me that there is probably a particular degenerate case in the mathematics underlying the code that lies at the source of all this; I'm tempted to guess at a division by zero problem, but that's pure speculation.
Anyway, to take advantage of the bug, you need to go from south to north along the wall, strafe-running at just the right angle alongside it, pressing up against it. The less you actually move into the wall, the more pronounced the effect will be. Speed-ups of three or four times can be achieved, although I haven't seen any precise figures.
This tactic was made most use of by DooM LMP speed-runners in order to get faster times. However, occasionally the effect could be used to good effect in DeathMatch too.