Among snakes there are venomous and nonvenomous types. The venomous snakes are the primary dangers, and the vast majority of them are broken into the elapids and the vipers. Among nonvenomous snakes, the only real dangers are the huge constrictors. Their bites deliver no venom, but can cause infection and the larger constrictors can kill via suffocation.
Among venomous snakes, the most common in the United States are the vipers. The only elapid in the US is the coral snake. The vipers are your rattlesnakes, cottonmouths, and copperheads. Vipers are noted by having large hypodermic like fangs that are hinged. When the snake strikes outwardly, they then stab the victim and inject venom.
Among the vipers, dry bites are somewhat unusual. It has been estimated that around 20 percent of viper bites are dry. While these figures are far from hard and fast, they give an idea about how you can get bitten by a rattlesnake and have no ill effects. (always assume the snake has injected venom and get medical attention though)
Among the elapids, the dry bites are often much more common. The reason for this is partially because of the fact that many elapids have rear fangs that are much smaller than their viper cousins. They make up for this by having more toxic venom in many cases. Still, the fact that they have more trouble biting cleanly as a group means more dry bites.
Why do snakes deliver dry bites? Some think it is because they are conserving their venom for prey they can actually eat. Some say that it is because their supply may have been just used on a prey item. Some say it is just an accident and the snake did not bite cleanly. The truth? Probably a combination of all of these in some form or fashion.
Even a dry bite can cause medical problems however. All snake bites carry a risk of infection. For this reason, you should get any snake bite checked out by a medical professional as soon as possible. Better safe than sorry, dry bite or not.