First of all I'll deal with the Special Attacks. These are essentially finishing moves that require a great amount of power to use but often finish of an opponent unless they are able to avoid it or block it with another attack. These are unique to each character and cannot be duplicated.
That said, on with the actual attacks.
Here are the techniques used in the game and their descriptions.
12 Eyes, Body Change, Instantaneous Movement, Solar Flare, Time Freeze, Zanzoken, Hide KI, Sense KI, Flight, Telepathy
And here are the attacks :)
Big Bang Attack, Burning Attack, Chou KameHameHa, Crusher Ball, Death Ball, Destructo Disk, Eye Laser, Gannet Gun, Genki Dama Kaioken, Kakusandan, KameHameHa, Kikouhou, Masenko, One-Finger Beam, Racoome Boom, Renzoku Energy Dan, Special Beam Cannon, Spirit Bomb
12 Eyes
This is a technique used by Tien where he splits himself into four different entities. Each Tien entity created can fight and be attacked. The only problem with this move is that each of the four entities of Tien only has a quarter of the power and the speed than if there was only the one original Tien. Later in the series Piccolo and Cell learn how to use this move also.
Big Bang Attack
A huge bolt of incredible destructive power, used only by Vegeta. In fact it was one of the first attacks Vegeta developed as a Super Saiyan. He holds one palm flat, directs it out towards his enemy and then launches the devastating blast. It is the way that he finishes many opponents off.
Body Change
The leader of the Ginyu Force, Captain Ginyu, uses this attack. He spreads his limbs out, and then shouts "Change Now!" shooting out a bolt of energy, and when contact is made with his target, he changes bodies with that person. After that he gains the strength and speed of his target, but not his own special techniques. After changing bodies, Ginyu can still do yet another Body Change if he should choose to. It is first introduced to DBZ in the fight between Captain Ginyu and Goku.
Burning Attack
This is Future Trunks' trademark attack. After coming back from the future, during the battle with Frieza, he first introduces this awesome manoeuvre. He holds out both hands forward, index fingers and thumbs touching, and then unleashes a powerful energy blast. This is the attack that finally killed off Frieza for good.
Chou KameHameHa
This is almost an exact replica of the KameHameHa, but with a couple of differences. It is far more powerful, and is capable of causing more extreme amounts of damage. The downside is that it takes far longer to charge up, and cna in fact take a toll on your body. It also uses a lot more energy, meaning you can't maintain it for as long as a regular KameHameHa. This is outdated as the series goes on though, with bigger and better attacks such as the Genki Dama (Spirit Bomb) being learnt.
Crusher Ball
An attack performed by Jeice, a member of the elite fighting squad known as the Ginyu Force, the crusher ball contains an awful lot of power. It is a large ball, about the size of a basketball, which is bright in tone, and orange in colour. Jeice balances this on one hand, then throws it at his opponent. This is his special attack, and we see him use it against Goku, narrowly missing, but causing enough distraction for Ginyu to gain the upper hand.
Death Ball
This is a small ball of energy that Frieza can create from either the tip of his finger or with both hands. While small, it is very powerful, and can even destroy planets. In fact he used this attack to destroy both Planet Namek and Planet Vegeta (Goku�s home planet). He also attempts to destroy Planet Earth with this monstrous technique, but is soon to be prevented by Future Trunks.
Destructo Disk
This in my own personal opinion, is one of the most effective attacks in the whole DBZ series. It is a flat, disc-shaped energy blast, which can be used to slice through its target with deadly accuracy. Krillin was the first person to have ever possessed this incredible technique, and has the skill to control the destination of the attack as well. He would have killed the almighty Nappa, during the battle with the Saiyans on Earth, if it weren�t for Vegeta warning Nappa at the last moment not to touch it. Krillin also uses this attack to slice off Frieza�s tail during the battle on Namek. Many other DBZ characters like Vegeta, Frieza, Cell and Android 18 have their own variations of the �Destructo Disk�.
Eye Laser
This is an attack which can prove very useful to the user. The attacker concentrates his or her energy, then lets loose with two compact beams, one from each eye. The strength of the beams is dependant on that of the user, but it tends to be powerful enough to finish off opponents of approximately the same strength. The first time we see anyone using this is when Piccolo does it whilst training Gohan. It doesn't cause any damage to him, but that's because Piccolo purposely made it weak. Frieza can also use this technique.
Flight
One of the most useful and fundamental techniques. This allows the fighter to fly and to hover above the ground using his energy. More energy is used up while actually flying though and a person flying can easily be picked up be a Scouter or the Sense KI technique.
Gannet Gun
The Gannet Gun is basically Vegeta's answer to the Kamehameha. He powers up the blast exactly like the Kamehameha, but when he releases the blast, his hands are both palm-forward. It truly looks quite awesome, but not quite enough to beat Goku�s Kamehameha in the Saiyan Saga.
Genki Dama
One of Goku's most powerful techniques, which he learned from King Kai while training in the �Next Dimension�. The Genki Dama (Or Goku's Spirit Bomb in English) is a large ball of energy gathered from every living life source in the local surroundings, which lend him their energy. However, the main weakness that this attack possesses is that it takes a lot of time to gather the energy for a Genki Dama. Whilst he sticks his arms up in the air, preparing to receive all of this energy, Goku is defenseless and open to attack.
Instantaneous Movement
This is one of Goku's most popular techniques, one that essentially allows him to teleport to any place where he can sense KI. He learnt this whilst on Yardrat, after Namek had exploded. He uses this a lot in the series, and in films too, as it proves a useful ally to him.
Hide KI
This technique allows the fighter to dampen his power level so that all of it is not picked up by a scanner device such as a Scouter or the Sense KI technique.
Kaioken
Taught to him by King Kai whilst training in the �Next Dimension�, this is primarily a power-up move. When Goku uses this technique, he flares up and gains a large boost to his speed and power. Goku can also use this as multiplied power to his Kaioken. At first, he shouldn't have been able to go past 2 x Kaioken without seriously endangering himself, as warned by King Kai, but eventually can increase the power of the Kaioken to around a 20 x Kaioken.
Kakusandan
Krillen used This technique during the fight with the Saibamen. He shoots a blast from each hand, controlling the blasts so that they merge and then directs it above the heads of his enemies. Thereupon he splits the blast again into many smaller ki bolts that rain down upon his enemies. A very effective technique which wiped out virtually all of the Saibaimen.
KameHameHa
The Kamehameha is a technique created by Master Roshi. It is a huge blast, which is charged up, and held behind the firer in cupped hands, then brought forward to release a large blast of energy. Goku later develops the ability to control the direction of the blast, shoot one from his feet, or with a single hand. He almost defeated Vegeta with this awesome attack, with the help of a little Kaioken. His son Gohan also learns to use this powerful move, as does Yamcha, Krillin, Tien, Goten, Cell, Cell Junior and Majin-Buu.
Kikouhou
The user places his hands to form a triangular shape, and then concentrates enough energy to power it up. He/She then rains down on the opponent with blasts of incredible power. It is used by Tien, and is his more powerful attack. The major downside to it though, is that because of its sheer strength, it drains the life force of the user, with the possibility of killing him/her. As long as the user stays alive though, they can fire as many Kikouhou's as they wish.
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. He uses this move fairly often in Dragon Ball Z.
One-Finger Beam
A fast, sharp cutting beam shop out of one finger, used by Frieza. This beam contains amazing power for its demeaning size, and can slice through almost anything. Cell also uses this attack, due to knowing all Frieza's techniques, and kills Trunks with it. Frieza managed to kill Vegeta and Trunks with his attack, although it wasn't strong enough to so much as hurt SSJ Goku.
Racoome Boom
Essentially a mouth beam, this attack is performed by the showoff member of the Ginyu Force - Racoome. He opens his mouth wide, and emits a blast of incredible power, capable of destroying much of the landscape. It is his most powerful attack, and almost kills Vegeta upon him using it. If he would have got a hit, it would have certainly finished the Saiyan off.
Renzoku Energy Dan
A machine gun KI attack, used by pretty much anyone who knows how to form balls or beams of energy. It is fairly powerful, especially if the defender is caught off guard, as many beams can be fired home, and the ones that hit have more power than the last. It is good as a distraction tactic too, firing a few of them before charging up a really big attack to finish it off. The disadvantage is that this attack can take its toll on the attacker, due to the large energy drain.
Sense KI
This technique allows a fighter to sense the power level of another fighter and judge thier strength. It is usful for searching for people over long distances without the need for a scouter.
Solar Flare
This technique is originally Tien�s. The user puts his hands in front of his face, says "Solar Flare," and lights up very bright, so much that he blinds his opponent. This technique was used a lot throughout Dragon Ball Z. Tien taught this move to both Goku and Krillin, which comes in handy during the fight with the Saiyans.
Special Beam Cannon
This is certainly Piccolo�s most powerful move in the whole series. A pair of penetrating blasts from two fingers, one going straight into contact, whilst the other coils around the first for drilling power. This thunderous attack can go through anything it hits, and eventually blows up when it hits something big enough. Cell and Cell Junior also learn how to use this devastating technique.
Spirit Bomb
An attack used by Yamcha, which isn't even close to having the power that Goku's possesses. It is far quicker to charge up though, and doesn't feed off the energy of the planet. We first see this used when Yamcha was in the room of Spirit and Time, fighting against some Saiyans. He gathered the energy in one hand, held onto his wrist with the other, and let rip with the beam, which didn't cause too much damage.
Telepathy
This is one of the most useful but hardest to learn techniques. If a telepath can train themselves properly then they can enter another persons thoughts and read their minds, sensing thier actions and diverting the targets attention away from the telepath, virtually hiding themselves in plain sight. Strong minds can overcome a telepaths will though, but it depends on the strength of the telepath. Telepaths can also comunicate with other telepaths through thier thoughts or plant thier thoughts onto a persons mind.
Telepathic strength is measured in Psi. All telepath players start with a Psi strength of 1 and must train up thier strength.