Believe it or not, the Judo Breakfalls/Ukemi videos contained on this page will give you, by far, the most important and frequently-used martial arts skills for your day-to-day life!
Most people (this certainly applies to me and my friends), when outside of the training hall, don't hang around high violence areas where their ability to fight is going to be frequently tested. In fact, in my career, my ability to breakfall safely and reflexively (apply ukemi waza) has, without question, been the most useful and practical of my martial arts skills.
Here's a quick rundown on the key concepts that apply to all
The main idea behind breakfalls is to spread the area of impact out over as large a portion of your body as possible in order to reduce point-loading. If you try to break your fall by reaching down with your arm, you stand a good chance of breaking it (your arm, not your fall!), but if you land more flatly with your entire side, leg, and flat arm taking the force, chances are you'll be fine. As surface area decreases, pressure increases (assuming the same amount of force is applied) - this is why someone punching you through a phone book (large surface area) doesn't hurt at all, why a pointy stick DOES hurt (much smaller surface area, therefore greater pressure), and why a sewing needle jabbed at you with the same amount of force will go right in easily (TINY surface area). So spread the forces out over as much of your body as possible and have everything impact at the exact same moment.
Keep your chin tucked tightly into your chest at all times when doing Ukemi. This will help prevent your head from hitting the floor (not a desirable thing at all!).
At the moment of impact, exhale strongly. Make a sound - anything will do, but an "Oof!" works well. At our old Dalewood judo club, some of the members had been taught to shout "Kiai!" when breakfalling... perfectly effective at letting your air out, but was so silly that I had them change to anything that suited them except for "Kiai"... Why? "Kiai" translates directly to "Spirit/Power Shout", so we effectively had a bunch of people doing the Japanese equivalent to an English speaker yelling "Holler!" every time they did a breakfall! The main point of letting your air out at the point of impact is to reduce the stress on your body. It's much better to release your air on your terms than to have it knocked out of you! To emphasize the point, I used to do a demonstration with a paper bag - fill it with air, hold the neck loosely, give it a smack, and all the air rushes out - no damage to the bag at all. But if you hold the neck closed tightly (as in a judoka holding their breath when falling), give it a whack, and it makes a Loud Pop! I much prefer my students to not POP! when they breakfall, and I've found over the years that many of them appreciate that sentiment!
Give the mats a solid slap as you land. Some of the breakfalls will emphasize slapping the mats with your arms more than others. The reason for the slap is to absorb more of the force of the landing in your arms rather than in your core body. Taken to an extreme situation, if falling from a height or thrown energetically onto a hard surface such that damage is inevitable, it is better to sacrifice your arm to protect your internal organs. Generally, though, it just shifts the force of impact (particularly noticeable with Mae Ukemi - Front Breakfall) away from your chest/gut, to your arms, and make the breakfall as painless and safe as possible.
Never reach for the ground with your arms when falling! Reaching out is a good way of getting an arm broken. When in mid-air, try to relax, align your body so as to spread the impact over the greatest surface area, and wait for the ground to find you... it always does, so there's no need to reach for it!
Practice, Practice, Practice. You've got to be able to breakfall as a natural reflex.
You know you're getting proficient at Ukemi when you don't shudder at the thought of
being thrown with a standing Kata Guruma, and you probably are proficient when a larger partner can throw you with Hane Makikomi fully and land on you, without your taking any damage.