Super Saiyan 1 -- The frequently mentioned Super Saiyan, is a change in which Saiyans and part-Saiyans sometimes under go. When there is trouble, a Saiyan will transform, and his/her hair will turn gold and the eyes will turn green. There is a enormous power increase. A requirement to become a Super Saiyan is to have a pure heart. So one with a heart PURE of EVIL can achieve this state also.
Super Saiyan 2 -- The second state of Super Saiyan. The hair turns gold and grows a little longer than in the regular Super-Saiyan mode. In this state, power can be adjusted to the Saiyans liking. For example, he can become very fast, but it may detract from his power. Kind of like a trade-off.
Super Saiyan 3 -- Goku's face becomes leaner, his hair turns gold and grows down to his waist, he magically loses his eyebrows, and he gets very strong. He also gets very tired after fighting in this mode for an extended period of time, for the great power output drains the user fast.
Super Saiyan 4 -- SSJ 4 is the last and final stage of a Super Saiya-Jin. This stage is called "Beyond Super Saiya-Jin". To become a SSJ 4, the Saiya-Jin must have a tail and plenty of strength (so the Saiya-Jin can expand it's current strength and power to get to SSJ 4). Like the very beginning, when the Saiya-Jin looks at a full moon, he/she is instantly turned into a Gold Oozaru, or a big monkey. While the Saiya-Jin is in Oozaru mode, he/she goes berserk to expand it's anger and strength, hence becoming SSJ 4. SSJ 4 is not a big monkey, SSJ 4 is actually transformed back to a human like Saiya-Jin.
Kamehameha -- A power blast (perhaps the most famous attack in dbz). The hands are brought to one side of the body, where energy is gathered. Then, the hands are thrusted forward, palms facing forward also, and the blast is released. Originally, Kamesennin was the only one that could do this, after 50 years of training. Goku picked it up just by watching (Goku also learned how to "remote control" it). Later on, a number of other characters start using it. Can translate to "Wave Attack of the Turtle School".
Kaio Ken -- Kaiou-sama (King Kai) had taught Goku a series of techniques that can raise his power, but cuts his endurance by the same factor. There are a series of Kaiou Ken levels, each respectively multiplying his power. So Kaio ken X 3, would be 3 times his normal strength.
Big Bang Attack -- One of the first techniques Vegita developed as Super Saiyajin, the Big Bang attack is a huge ki bolt of incredible destructive power. Vegeta holds one flat palm forward towards his enemy and launches the bolt. The attack that took out Artificial Human #19
Body Change -- Ginyu's ability to switch bodies with whoever he wants. When he is within reasonable distance, and yells as he shoots a beam from his mouth into his opponents.
Bukuujutsu -- "No Air" This is name of the technique used when people fly around.
Daichi Retsuzan -- Frieza's slashing energy attack. He put his arm across his body, charges the attack from his two fingers, and does a swiping motion with his arm creating a cresent wave. It covers a very long but thin area, and will cut almost anything.
Genki Dama -- "Life Force Sphere," or "Spirit Bomb." Goku needs lots of time to gather the energy from the living things on the planet around him. The more energy available, the bigger the sphere. This can only be performed in normal mode -- Super Saiya-jin can't create a Genki Dama, but they can use the energy from it if it already exists. It's not so much an energy attack, as it is a matter of throwing a small star at someone.
Frieza Beam -- This is Frieza's trademark technique. It is a beam of energy shot from one finger, and does not explode on impact. Instead it is a piercing attack which continues through its target and can also be used to slice. This was used to kill Dende and Vegeta on planet Namek.
Fusion -- A process that allows two people to become one, creating a very strong being. It's not a permanent condition. It requires that the two be of near-equal power, and that they both have a certain amount of prepping. Includes having to go through a stupid-looking set of dance steps.
Kienzan (Destructo-Disk) -- Kuririn's "slashing energy disc", developed to combat Nappa and Vegeta. Vegeta and Frieza have been seen to use this attack also. The arm is extented up, with the palm facing up in the air, and the disk is formed. When launched, it can practically cut through anything. This allows weaker characters to have an advantage over stronger ones if they know how to use it.
Makankousappou (Special-Beam Cannon) -- Piccolo's screw blast. Actually two separate blasts, one being the straight-shooting beam, and the other coils around that. Very powerful, but requires some time to build up the energy first. "Screw attack of the Devil"
Masenko -- This is Gohan's trademark energy blast, and is fairly powerful. Gohan powers up a blast over his head with both his hands, one palm behind the other, then brings his hands down in front of him to fire the blast. Gohan used this blast fairly often during the second series, especially during the Freezer saga.
Sansouken -- A fake, where the attacker moves so fast that an after-image is left behind. Goku has been able to leave three images of himself.
Shunkan-idou -- The teleport ability that Goku learns on Yardrat. But, he can only jump to a place where someone he knows is located (he has to feel that person's energy to teleport to that place.)
Sou Ki Dan -- "Energy Bomb." Yamcha's remote-controlled energy ball. Later, Goku learns to remote-control his Kamehame-ha bolts.
Super Ghost Kamikaze Attack -- Gotenks (Goten and Trunks fused together) spits out a ghost of himself. The ghosts explode on impact, which can then do damage and drain your energy.
Taiyoken -- This is a blinding attack used by Tenshinhan during the Tenkaichi-budoukai, and others later on. With the hands spread across the face, the entire body can glow with a very intense light, blinding the opponent. Translates to "Sun Technique."
Time Freeze -- A technique known to be used only by Guldo, one of the Ginyu Force. He can literally freeze time, and uses this time to attack or surprise his opponent.