How to Minimize Injury when Crashing

The most important thing to do when you crash is to protect yourself as much as possible in order to minimize injury. I think this statement is rather obvious. Knowing this is the easy part, knowing how to do this is harder, and being able to do this is the hardest.
To protect yourself when crashing, do the following:

Realize you are crashing and think about the following things to do.
Don't let go of the handlebars until you've already hit the gound.
Tuck your head down, pull your elbows and knees in.
Relax for the impact.

Realize that these steps start after you have committed to crashing, i.e., you have already attempted to avoid crashing and are on your way down. Before committing to crashing, you should be doing everything you can to avoid going down.
The first point is very important. The following points are very unnatural and will be close to impossible to do if you don't realize that you need to do them. With proper preparation, this realization can be close to instantaneous.
The second and third points coincide with the "tuck" of the "tuck and roll" you may have heard of. The big thing here is to get your body and limbs contained instead of flying around begging for injury. Think of what happens if you reach out with your hand when you're crashing (a very natural thing to do). You are falling so you reach out with your hand. When your hand hits the pavement, it stops. The problem is you are still moving forward. This causes your face (which is looking where your hand is reaching, instead of being tucked down) to slam the pavement. It also puts a great bruise and abrasion on your palm and a lot of stress on your collarbone. It sure is a lot easier on your body if you just end up falling on your shoulder!
If you are able to make it through the first three points, the last one, relaxing for the impact, is actually quite a bit easier than it sounds. It's easy to understand the benefits of relaxing. If you are relaxed, your body and limbs will be able to move with the dynamics of the crash. If you are tense, they will be forced to move with the dynamics of the crash, i.e., injured.
Now you know what to do in a crash and how to do it. In order to be able to perform the above steps during a crash, you need to practice doing them. There are a few ways to practice crashing without actually going out and crashing so I wouldn't get too worried here.
Find a soft area like a nice lawn or a wrestling mat and practice tucking and rolling. Start out squating so you are nice and low to the ground. Be sure to practice rolling on both your shoulders. As you gain skill, you can do tuck and rolls from a more upright position. Doing other activities that cause you to fall a lot are also beneficial. Growing up I played a lot of soccer and did a lot of skiing in the winter. Between these two activities (and others) I would fall hundreds of times a year. If you fall enough, you will get good at falling in a protective manner.
Once you are fairly comfortable with a tuck and roll, it's time to simulate crashing on your bike. It's easiest if you have a friend to help out here. Find a nice grassy area with a slight hill. The hill is used to shorten the distance you will fall. Start out on the side of the hill, with the hill to your left. Get on your bike. Your friend will straddle the rear wheel and hold your bike upright. With your friend holding your bike, clip your feet in your pedals and get in a riding position. It's probably best if your cranks are parallel with the ground. Now pretend you are riding along and you start to crash. Realize you are crashing. Hang on to your handle bars, tuck your head and pull in your elbows and knees. At this point, your friend should let you fall to your left (towards the hill). Your friend needs to make sure that he/she steps out of the way of the bike before the bike is let go, otherwise your friend may end up getting wacked in the leg by your bike. Once you start to fall, be sure that you continue to hold onto your handlebars and keep everything tucked in and relaxed. Repeat this a number of times to make sure that you can fall correctly. If you are feeling adventurous, you can also try falling to the right with the hill to your right instead of the left. There is a minor risk of damaging your derailleur and bending the part of the bike where it attaches though so it normally isn't recommended.
Happy cycling,