This video gives you an example of the traffic in Cairo, and you can find many more on YouTube or a similar site (e.g. search for "cairo traffic").
Note the noise, the randomness, and the pedestrian calmly walking across (about 1m25 in to the video). Note how few vehicles have headlights on (some have side-lights on, some flash high beam every now and then), or use indicators. Buses generally get something like right of way (and bigger bus trumps smaller bus).
And yet ... well, there are accidents, but not nearly as many as you'd think from seeing it or being driven around in the middle of it. There were two while rwrylsin and I were wandering around town, but I suspect one of those was caused by a spot of rain making the dusty road rather more slippery than the drivers are used to. rwrylsin prefers to think of crossing the road there as being something like a game of Frogger - I don't, because I'm rubbish at that game. Instead, I kept thinking "I am a leaf on the wind" and just sort of drifting across, waiting for gaps and pauses and hesitations from drivers.
Being driven around in a taxi was also an interesting experience, for very Chinese values of "interesting". Drivers there are apparently aware to the nearest millimeter where the surrounding cars are, and use this to squeeze through gaps where any sane person would wait. Lanes are truly optional, and overtaking can be done on either side. The car horn becomes a fairly sophisticated signalling device in the hands of the Cairo driver, with patterns of beeps conveying variously "Hello", "I am about to overtake", "I am beside you, don't move", "Coming through, get out of my way", etc. Vehicles also seem to stop wherever they want, to pick people up or drop people off or simply to park, and the rest of the traffic just flows around (after much more horn beeping, of course).
Pedestrians are almost everywhere, often walking along the side of the road, equally often randomly walking across them. There are also bikes, trikes, horse-drawn carts (and donkey-drawn and goat-drawn and human-drawn) too, especially in the narrower streets.
One of the most amazing bits of driving I saw was an area where two fairly wide roads (maybe three lanes in normal places, so three to six actual lanes in Cairo) merged and then split again maybe two hundred metres later. Of course, many of the cars coming from the left side pre-merge wanted to leave on the right side post-merge, and vice versa, and the overall effect was like one of those precision driving teams weaving in and out of each other - only without any precision, just a never-ending series of near misses and a whole lot of horn beeping.
So, driving in Cairo - you don't have to be batshit crazy to drive there, but ... actually, I think you do !