Command Jump
This neat move lets you jump up unexpectedly, from there you can dash out or initiate your flurry kicks!
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, opening new combo possibilities.
Knuckle Smasher
A good solid body check! It hits twice when close enough.
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. In the latest iteration, you can hold the SP button down to have the laser out longer and do more hits with it.
Savage Sweep
A simple sweep kick that trips the opponent.
Handstand Kick
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 opponent 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. And he can cancel into the Rapid-fire Kick.
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.
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
Piccolo dashes forward with a sliding side kick, lifted straight from the classic Super Butoden games. On impact, the opponent flies back quite far. When hit within a combo or on counter hit, they 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.
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 opponent 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. You can only use the Mystic Harpoon once per combo. The second time you try to use it it changes from being a long-range grab into a long-range punch, knocking the opponent down.

The EX version is a great move as you can combo into though it is also a combo ender. 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.
Mystic Air Harpoon
This new move is an anti-air version of his stretchy-arm grab. Though it doesn't work exactly the same. Instead of being a reset, this slams the opponent down on the ground. The EX version ends with an autocombo much like the horizontal version and ends with his Mental Shock, which was removed as a stand-alone move.
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.
Halo Stomp
Another Piccolo classic. From the air, he shoots down (on a steep angle with the Light 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. You can special-cancel into this after you hit the opponent with an aerial Destructive Wave. 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. Also, once you've hit with the EX version, you can air dash to keep on the pressure.