Double Claw
Excellent follow-up to his single claw slash, great range as well. You don't have to connect with the first slash to be able to throw out the second one. Chains into Carnage Blitz (both normal and EX versions), EX Destructive Wave and EX Mystic Harpoon, as well as Supers. Later updates have included the ability to dash-cancel from the second claw attack, either when whiffed or connected, allowing you to keep the pressure on.
Knuckle Smash
A good solid body check! It hits twice when close enough.
Knee Smash
Knee to the face!
Jumping Knee (launches)
When the first knee attack hits, you're able to perform the jumping knee follow-up, which launches the opponent. You recover a bit later than with the Crouching Strong Kick so your flow might need to be adjusted a little, as you'll have slightly less time to plan your follow-up.
Eye Laser
A move hinting at Piccolo's demonic background, a shadow briefly engulfs him as he shoots out a short-range eye laser towards the ground, stunning the opponent. It stuns them long enough for you to start a combo chain after it hits. You can't chain into this from a medium attack as the start-up is too slow.
Handstand Kick (launches)
A tool for launching the opponent, though in a flip-KO fashion. Not really dependable as an anti-air attack.
Kick Fang
A downward-directed aerial kick. Stuns the opponent when they're standing, but punts the enemy down when they're hit while in the air. Piccolo dismounts upward after connecting. A very short while after the dismount, Piccolo is able to perform any aerial move to keep pressuring the opponent.
Rapid-fire Kick
Flurry kicks, these keep Piccolo suspended in mid-air. You can hit the opponent a couple of times before they're automatically knocked away. Great pressure move.
Elbow Drop
Alternate jumping punch, angled directly under him. Does a bit more damage then his regular Jumping Strong Punch and causes a hard knockdown on impact.
Solar Kick
Alternate air kick. Is faster and has more forward range then the default jumping strong kick, but goes on kind of a weird angle. Probably best for air-to-air situations.
Sonic Kick (wall-bounces)
Piccolo dashes forward with a sliding side kick, lifted straight from the classic Super Butoden games. On impact, the opponent flies back quite far and will bounce off the wall, perfectly setting up a juggle follow-up. It has a combo limiter, in this case meaning that performing the Sonic Kick a second time in the same combo will just knock the opponent away rather then wall-bouncing them again. You can combo into this from the Focus Attack but also from basic attacks. Standing Strong Kick into Sonic Kick in particular is very good.
Zetto Jumpo
An extra, unique Zetto Counter for Piccolo has been added; this counter lets him jump straight up right after blocking an attack allowing him to either escape with an airdash or attack with a jump-in.
Destructive Wave
Piccolo's main zoning tool. A medium-to-far ranged energy spark is shot out of his hand. While it doesn't travel like a regular Ki Blast, it's range makes up for that, though all versions have a bit of charging time. Weak punch version comes out the fastest and doesn't knock the opponent down, Medium version takes a tad longer and knocks the opponent away, and the strong punch version takes the longest but also has the hardest knock-away effect on the opponent, causing them to twist around. EX version comes out very fast (and produces a larger energy spark as well) and knocks the opponent away even harder, causing them to flip around and fall down hard. These differences also translate to the aerial version, which Piccolo fires diagonally downward. As the spark causes him to recoil backwards the range is reduced a bit.
Mystic Harpoon
A must-have Special move for Piccolo. He extends his arm in an attempt to grab the opponent, after which he pulls them towards him, leaving them stunned, a perfect set-up for any attack or combo. You can even grab falling and airborne opponents, resetting them. None of the normal versions can be combo'ed into (apart from grabbing an enemy after launching or bouncing them).

The Weak punch version has the least range, as Piccolo doesn't even stretch out his arm. The Strong punch version has the best range, just shy of full-screen range. The medium version, as you'd expect, is somewhere inbetween.

The EX version is a great move as you can combo into it, it's a cool and stylish combo finisher. It has the Strong punch version's range. Upon grabbing the opponent, they're dragged towards Piccolo and met with a heavy gut punch followed by a launching knee attack and finished off with a demonic Mouth Blast, which knocks them away. When performed during Demon Mode, the Mouth Blast is replaced by a slightly more powerful Eye Laser. All versions are blockable, so technically it's not a grab. Master this move to master Piccolo. You can grab and break a Ki Blast with it as well.
Carnage Blitz
Tank move, Piccolo charges forward with a shoulder attack and he's able to plow through Ki Blasts during this part, though you're vurnerable to attacks before and after the dash. Upon hitting the opponent, they are knocked away. The Weak version has the least range, while the Strong version has the most, as to be expected. The EX version has a little more to it, as upon impact with the shoulder attack (succesful or even when blocked), Piccolo teleports behind the opponent and then delivers a powerful spartan kick, smashing the opponent away. To make sure he doesn't miss them, he does a big axe kick as the follow-up after hitting an aerial opponent with the EX Carnage Blitz. In Demon Mode the Light and EX versions both have armor on startup as well.
Mental Shock (shocks)
Anti-air attack. Piccolo sends a current of electricity out of his antennas. Upon hitting the opponent, they are temporarily frozen in place in a shocked/electrified state. This leaves you with enough time to perform a follow-up attack. Has a limiter to prevent infinite loops. All versions are identical and it has no EX version.
Halo Stomp
Another Piccolo classic. From the air, he shoots down (on a steep angle with the Weak version and a wide angle with the Strong version), with a diving kick. Upon contact, he explodes into a flurry of downward stomping kicks, the last kick knocking the opponent down. The EX version ramps it up a little by adding more kicks and thus doing more damage. The EX version also has an alternate ending kick by holding Up, knocking the opponent down rather then away and allowing you to still move or attack in the air after dismount.