Clearly this guide is meant as an aid memoir and you should not attempt any of these without supervision from a qualified instructor. We cannot be held liable if you hurt yourself doing them. That's just evolution in action! We do expect you to learn the Japanese name for each breakfall but the kanji is there for fun.
What is ukemi?
Some terminology first. Ukemi can be translated as receiving body (受け身) is what uke (whoever receives the technique) does when nage (投げ fall) or tori (取り, receiver of attack) applies a technique. Note that the kanji is there to make sure the right Japanese term is used. If you happen to read Japanese and notice a mistake, please let us know! Onwards to what is break falling. Break falling is a way to safely escape a technique that could impart serious harm to the receiver. It is self defence at its most basic form. For obvious reasons, without it, one cannot practice Aikido safely. Thus, it is one of the first things students should learn to do well. The following drills were designed to teach drills that once put together lead to superb break falling. These break falls will be both safe and pretty. There are two stack exchange question about this: the etymology of ukemi and why we do break falls. You are cordially invited to add your own answer.
Basic Ukemi
A guide to making your basic (aka everything from beginner to Shodan) ukemi better. These are all the break falls you need!
Koko ukemi (Back) 横受け身
1 Stepping back. Arch backwards, keeping your head tucked in, and step backwards before falling. 2 Punish the mats. Lie down on your back, knees bent and feet flat. Hands start crossed over the chest and extend to 45 degrees and slap the mats. The mats are evil and must be punished. 3 Core. Lie on your back, kick your legs up and hold for as long as possible. You are aiming to balance on your shoulder blades. This builds core power. 4 Get ups. From crouching, roll backwards. Throw your legs and arms forward and get back to kneeling without using your hands. If you cannot do that, ask a helping hand to give you a tug before coming back to kneeling. 5 Kneeling roll. Crouch down, throw your shoulders back as in the stepping back exercise, roll remembering to punish the mats, and get up as you did in the get ups step.
Yoko ukemi (Side) 後方受け身
1 Side to side. Lie down on your side in the correct landing position: both feet pointing in the same direction, both arms on the front of the body. Kick your hips upwards and around. You should be in the same finishing position but on the other side. 2 Punish the mats. Same as side to side but hit the mats five times on each side. 3 Crouching. From crouching, move one leg to the side across your body and roll on the opposite side. 4 Get ups. From the finishing position, tuck your lower leg under and use it to push yourself up. Do not use your hands. 5 Run backs. Standing up, keep looking forward, and run backward veering to one side. When you lose your balance, do a yoko ukemi on that side. Get up still facing the same way as you started.
Zempo kaiten ukemi (Forward roll) 前方回転受身
1 Wheel plank. Arms are in a wheel position, fingers pointing to each other. One knee is on the ground, toes tucked under. The other leg is straight. Once in equilibrium, straighten the bent leg and hold. Make sure you do both sides. 2 Kick ups. Arms in the wheel position as above. Lift up the back leg and hold. If you can, kick with the front leg to gain more height. 3 Get ups. Lie in the finishing position, leave your feet where they are, and use your arm to push your hips upwards until they are over your feet and stand up. 4 Knee roll. Both knees down, put one shoulder on the ground, and the same arm pushes the opposite knee back. Kick with the back leg and roll. Remember: tuck your head in! 5 Crouch roll. One knee on the floor, same arm goes forwards, and kick from the back leg to roll over. 6 Swiss roll. Grab an exercise ball, hug it with your arms, and put your cheek on it. Lean foward to place the ball on the ground and roll over it. Do not let go of the ball.
Tobu ukemi (Flip) 飛び受け身
1 See saw. One leg forward, same arm bent so the palm is upwards. Point your head to the floor and move the back leg up making sure your back is straight. 2 Flip. Sit on all fours, present one arm underneath your body, and let your partner grab it. Whoever grabs the arm has their legs bent and a straight back. Then, they pull the arm up, causing you to flip on your side. thus landing in the perfect position. 3 Roll. This time your partner is kneeling down, you are grabbing their belt with one hand palm up. Put your shoulder on their back and flip over them. 4 Belt roll. Your partner is standing up, you are grabbing their belt knot with your hand palm up. Do the same exercise as the see saw above twice and flip on the third.
Mae/Zempo ukemi (Falling leaf) 前受け身 or 前方受身
The falling leaf break fall is sometimes called just mae (front) or zempo (forward) but without the kaiten (which means rolling). However, there does not seem to be any consensus on the matter as this stack exchange questions shows. 1 Swan. Start off in the plank position, lower your hips down keeping your thighs off the floor then lift alternate legs. 2 Lower down. Start off in the plank but aim for your hands to be underneath your shoulders. Lower yourself to hover just above the ground, keeping your elbows tucked to your side. 3 See saw. Lie face down flat on the floor, arms extended forwards. Lift your shoulders and hands up. As you bring your shoulders and hand down, lift your legs up. Then do the opposite. 4 Downward dog. Feet on the floor, hips up, and hand down on the floor. Lift one leg up so it is straight then lower your chest to the floor looking to one side. Then roll your legs as in the see saw. If this is too easy, kick the support leg up. 5 Kneeling. From kneeling, one shoulder goes to the ground, the opposite arm serves as support. Look to the support arm and kick your legs upwards. Bring the legs down in the see saw motion. Katate sokuten ukemi (Half cart wheel) According to this stack exchange question. this is the best way to describe this break fall in Japanese. Katate means single-handed and sokuten means cartwheel. This is the break fall that you will do when receiving oshi taoshi. 1 Feet clap. Stand one leg forward, hands on the floor with the same hand as leg forward. Lift the back leg up. Kick upwards so that your back leg touches the front leg. 2 Side jump. in the same position as above, jump upwards, and move to the side so you land at 45 degree from your starting position. Remember to clap. 3 Oshitaoshi. Your partner holds your forward hand up as in the finishing position of oshitaoshi. You do a side jump but this time only one of your hands is touching the floor.