Many of you have probably seen this video or something like it.
That video definitely wasn't shot in Delhi--the rickshaws here are green with yellow canopies, not the other way around. Traffic in Delhi (at least, in south Delhi) never gets quite as crazy as in that video, for a couple reasons. First, there's a lot more traffic here, so there isn't enough space to do the kind of shenanigans in the video, and traffic doesn't move as quickly. Second, Delhi has stop lights, and people obey them (more or less). An intersection like that in Delhi would definitely have a stop light.
Other than those differences, however, that's a pretty accurate portrayal of Indian traffic; to a Western eye, it looks like total chaos, with everyone fighting to get to their destination as fast as possible. In truth...well, in truth it's still pretty chaotic. Driving on the left is more of a suggestion than a rule, and lane markers might as well not exist. However, there is a code of conduct, and people do actually get upset if you violate the code, so it's not totally lawless. Here are a few of the rules that I've noticed; you can re-watch the video above to see if you agree.
The first rule, however, is something you can't really understand from the video because the sound is soft, and that's the use of the horn. Everyone is constantly communicating with their horns--every time you pass another vehicle, you give a toot of your horn so that they know not to pull to one side. Most large vehicles, like trucks and buses, actually have "Horn please" written on the back fender to remind you to follow this rule. This is basically the exact reverse of the Western rule to check your blind spot before changing lanes; in Delhi, the rule is to notify someone if you're in their blind spot.
The second rule is a little harder to state clearly, but the basic idea is that you're entitled to any space on the road that you can get to without making someone else come screeching to a halt. That is, it's perfectly okay to drive out in front of oncoming traffic and force them to stop, but only if they're far enough away that they won't have to swerve into a lamppost (or more likely, another vehicle) to avoid hitting you. The other side of this rule is that if someone cuts in front of you, you have to stop, and in fact, people are willing to do that, for the most part.
The third rule isn't really a rule, but more of a property of the system. The distribution of motorcycles, rickshaws, cars, and trucks/buses is such that traffic jams tend to be self-regulating. This is because the motorcycles can squeeze into small gaps in traffic, forcing oncoming traffic to stop, which gives space for the cars and rickshaws to move in, which then creates space for the big trucks and buses (of which there are relatively few).
As an example, if you watch the video again, you'll notice that there's a pretty significant jam near around 1:30. In the West, if there was a steady enough stream of traffic and a yield sign, the poor driver with the yield sign would never get to take his turn. In India, it's different--watch what happens as traffic piles up behind the stream of cars turning right. Eventually, the motorcycle riders get impatient and start to edge their way forward (one of them almost gets hit by a white car who broke rule #2). They force the turning cars downward bit by bit, until eventually they pass the barrier, and no one else can turn. Then the traffic heading straight from top to bottom gets to go, until enough motorcyclists pile up in the right turn lane to start the process all over again.
So that's Indian traffic; it's pretty crazy, but it's not totally insane. Just don't try it while talking on your cell phone.