Kachü Tenshin Amaguriken - faster than a speeding bullet
Introduced in V5.10.
Cologne has given Ranma a pressure point jab that makes Ranma so sensitive to heat she can't turn back to a boy, but Cologne has a 'Phoenix Pill' that will cure Ranma. After a week of battling Cologne, she takes Ranma outside, and sets up a small fire. She then puts some chestnuts in the fire, and grabs them out so fast her movements blur, and she takes out all the chestnuts without getting burnt. She tells Ranma if she can master this, the Kachü Tenshin Amaguriken, then she'll easily be able to recover the pill. Ranma trains hard, and eventually she gets fast enough to recover the pill - though the first one was a fake.
Some time later, Cologne teaches Ryöga the Bakusai Tenketsu, which makes Ryöga very good at taking damage, and Ranma does a super-fast blast of hits on Ryöga, where he hits the same spot on Ryöga several hundred times so fast it looks like one hit. Ryöga gets hits though a tree from the power of the punch, but it didn't hurt him too much. However, Ranma never said he used the Kachü Tenshin Amaguriken as a specific attack, rather as he used the speed from training using the Kachü Tenshin Amaguriken. In the manga, this move is only mentioned in V5.10-11, and nowhere else does he do such a blast of hits as he did on Ryöga. But in the anime, Ranma uses the attack as a special move fairly often, though he often shortens saying it to just Amaguriken.
So, in the manga, it seems the Kachü Tenshin Amaguriken is a training method, and an indication of speed, and not an actual move, while in the anime, it is a special move.

Bakusai Tenketsu - why chew on rocks when you can break them with a finger?
Introduced V6.5, where it was shown by Cologne, used several times against rocks near Ranma in V6.7-8, and has also used it in, V24.5, V25.1, V27.9 and V33.5
To help Ryöga beat Ranma, Cologne shows him the Bakusai Tenketsu - she taps a boulder and it shatters (almost explodes) into small fragments. Genma explains to Ranma that the attack is based on the fact that everything has a weak point, and by hitting it right, you can destroy that thing. Cologne trains Ryöga by suspending him and a boulder each from a rope, and swinging Ryöga at the boulder, who then has to concentrate and destroy it with his finger else he smashes onto the rock. After a week of training, Ryöga can not only make rock explode sending shrapnel everywhere, but can take blows far more easier because of the training - he's gotten very used to being hit by rocks etc.
Since the attack only works on rocks and reasonable similar substances (it has worked on wood), but not humans, Ryöga doesn't use the attack much later, but does occasionally find it useful - he can practically tunnel underground with it.

Happö Daikarin - Happosai bombs away!
Introduced V11.4, and is used frequently.
When Happosai was training Genma and Soün he obliterated them after they tried to run him over with a boulder with his terrifying ultimate move. This also ruined a bra, and Happosai decided to 'bury' the move - he wrote it onto a scroll, then hit it under a boulder. Back to the present, one day Ranma, Genma and Soün all gang up on Happosai, who decides to use his ultimate move - which scares the hell out of Soün and Genma. But it doesn't work and Ranma wonders what Happosai was trying to do with his strange motions while doing the move. Happosai wants the scroll back, and the others want to stop him, but they have trouble as the boulder is in a women's open air hot springs, where Akane just happens to be. However, not even Happosai can read his own hand-writing because it's so bad, and tears up the scroll, but he does remember it after Ranma smashes him with a concrete grass-roller. Later, Ranma finds Happosai standing over Soün and Genma, who are both unconscious and burnt. Happosai then strikes a match and throws a small round bomb with a fuse at onna-Ranma. Since Ranma was carrying a tennis racket at the time, she just hits is back on him. The same happens with the next bomb, and Happosai makes a huge bomb (about 3-4m high), but Ranma just kicks him over a cliff with it. Later, a badly burnt Happosai is seen on TV - he did survive the massive explosion.
Happosai uses his little bombs quite often, and they can be very effective against even the most difficult of opponents. However, Ranma does use the move's weakness against Happosai when he can.

Hiryü Shöten Ha - Instant tornado, just add angry hot chi!
Introduced V13.4. Cologne used it on Happosai when they were both young - see V13.9, and shows does it on Ranma, Ukyö and Genma in V13.4. Ranma uses it on Ryöga in V13.7, Mousse, Kunö, the Principal and Happosai in V13.10, Herb in V24,1 and V25.1, Happosai and Lukkosai in V31.3 and used by Ranma's copy in V35.3 against Soün and Genma. Also used twice against Saffron, and in the last chapter, to break the Dragon Tap.
Happosai made Ranma as weak as a child by burning a special mark onto his back. Since only Happosai has the chart with the curse, Ranma must defeat him to get his strength back - as a note, he still has his speed at this time. While training in the with his dad, and Ukyö (who has come to cook, and use the opportunity to get closer to Ranma), Cologne shows up, and says she'll teach him the Hiryü Shöten Ha - a secret move of her village. She tells the others to attack, and some distance away, Akane who is walking to the site sees a huge flash of energy, and Ranma falls down to the ground right next to her. However, Cologne says that Ranma only has a 20% chance of learning the move in his current weakness, but he says he'll learn it in 3 days.
The training is hard and difficult, and the first part involves Ranma having to spiral in on his enemy while staying calm and cool. Genma's embarrassing photos of Ranma, and other distractions give him problems, but after training all night he has finally perfected the first part. The next part is to keep himself cold while standing on a rock in the middle of a hot spring, while being attacked by Ryöga (who wander by, and decides to help Ranma), and spiralling in. Ranma does well at this, but Cologne hits Ryöga for not attacking all-out as Ranma needs to use hot chi.
Later, Akane wraps bandages around her arms, and sets them on fire, to give Ranma the hot chi he needs, but her clothing catches on fire, and her top is ruined. However, Ryöga gets very pissed at Ranma for seemingly molesting Akane, but Ranma deliberately makes Ryöga more angry (eg "Sorry Akane, you're so cute I had to attack you") so he can get Ryöga to attack all out. This works a bit too well, and Ryöga punches Ranma into the side of the mountain, making a large dent. However, despite this, Ranma starts working on the move and begins spiralling in, staying cool, while channelling Ryöga's hot chi into into a spiral.
Just before Ryöga is about to kill Ranma, he unleashes the finishing move - a punch at the air using all the concentrated energy from Ryöga's chi. A blast of energy follows, and huge gusts of winds surround the area, and a tornado (which is perhaps over a mile high) is the centre. Ryöga falls from the sky, his clothing shredded, and almost dead from the injuries. Ranma isn't too well off either - he's sitting in the middle of a shallow crater, with spiralling inward cracks in the ground, with most of his shirt shredded.
The move uses your opponents' energy against them, though the resulting tornado can wander into others. The most dangerous part is the main blast of super-concentrated energy which will wreck anybody if they get hit by it, though anyone getting caught up in the tornado will probably loose consciousness (or at least get very dizzy from the high speed spin). People caught in the tornado often get flung out spinning so fast they can dig a hole in the ground.
Herb and Ranma are the only people known to have had a Hiryü Shöten Ha used on them without being hurt. Herb, a master of chi, knew of the deadly attack of Cologne's village, and uses cold energy just as Ranma executes the move, and just gets sucked up into the wind, but comes flying down the centre of the tornado an blasts Ranma. Later, Ranma deliberately tricked Herb into doing the same thing, but this time Ranma go sucked up - and he then came down, having collected a huge amount of energy and wipes out Herb. Note, the tornado can last up to a few minutes. In later volumes, Ranma has gotten better at using the move, and can execute it very quickly.

Shishi Höködan - I want you to know, I'm feeling very depressed.
Introduced V20.1. Used by Ryöga way over 10x in V20.1-5 on Ranma, and 3x in V33.3-5 on Ranma. He has used the full version about 7 times 20.4-20.6 on Ranma , and once in V24.7 against Lime. Ranma has used it once on Genma in V20.2, and about 8x in V20.2-4 on Ryöga.
While trapped in a cave, Ryöga tries to use the Bakusai Tenketsu, but it doesn't work on the loose rock. However, a civil engineer gives Ryöga a scroll explaining the Shishi Höködan. Later, Ryöga has challenges Ranma to a duel again, and beats him up for once, because Ranma couldn't get around the move. When using the move, Ryöga puts his hands together, palms facing outward, and at a right-angle to his arms, and a short lasting, large spherical ball of force and energy blasts out from his palms. The force knocks others flying, and is rather like being hit by a car, or truck.
Ranma can't figure out how the moves works, and gets depressed, but then blasts Genma, and later Ranma figures out the move is fueled by the heavy feeling of depression. Ranma and Ryöga both try making themselves as depressed as possible, but Ranma can't really compete with Ryöga - who is trying to work out how to perfect the move.
Ryöga realises he must be terribly depressed to use the perfect version, and also that he must channel the energy around him. To make him depressed enough, he gets Akane to tell him "I hate you". With this level of depression Ryöga can project a huge column of energy into the air (about 20m wide, and over 100m high), which then collects and comes down as a huge sphere (about 20m wide), blasting a massive crater into the ground.
However, Ranma figures out how Ryöga is not getting hit by the ball himself - he's letting his feelings go, and so by distracting Ryöga, he gets hit as well.

Möko Takabisha - are you confident enough to face a fierce tiger?
Introduced V20.5. Ranma has used it about twice in V20.5 on Ryöga, and once in V25.8 on Hinako, and a special double (one blast with each arm) in V25.9 on Hinako.
Ranma tries to make himself depressed to he can fight Ryöga with the Shishi Höködan, but it doesn't suit his personality, and after some persuasion from Genma he modifies the Shishi Höködan to create the Möko Takabisha, which is exactly the same, except fueled by the strong emotion of confidence.