Hadō: 波動 Surge
Ansatsuken's founding principle, believe it or not. The user focuses his or her will to gather a certain amount of ki and shoots it forth. Any other ki technique is just a different application of this principle.
This principle, as one might imagine, has seen a wide variety of uses and modifications, which have been listed from weakest to strongest. As new moves are introduced and current ones are modified, this list will always be subject to change.
Zanku Hadōshō: Performed by Oni. One of the few variations not used for attacking, Oni uses this for aerial mobility.
Gadōken: Performed by Dan Hibiki. He uses one hand for this, but fires a small ball of green ki which barely travels one foot (if at all) before dissipating. It's a bit more potent as an EX move. This is a decent way of breaking an opponent's offense, but pretty damn useless otherwise.
Hadōshō: Performed by Sakura Kasugano. A basic attempt that barely escapes Sakura's hands, but this can hammer the opponent good for 3 hits. Great for getting back on the offensive.
Shinkū Gadōken: Performed by Dan Hibiki. Somewhat more powerful, but the small distance gained makes this Super Art little more than a last ditch effort. Up to 3-4 hits.
Hadōken: Performed by Ryu, Ken Masters and Sakura Kasugano. This is how you do it right. The user channels his or her ki and blasts it forward. Out of the three warriors to use this standard version, Ryu's is the most potent. Ken only uses this move when necessary, while Sakura has to exude much more effort in order to put some distance behind hers (and her version is rather small to begin with, forcing her to charge up for more size/damage).
Gō Hadōken: Performed by Akuma, Oni and Gouken. This more powerful Hadōken is capable of a fatal blow if used in that manner. Gouken, of course, has gained enough skill to avoid killing. Moreover, both he and his demonically crazed brother are able to charge up the move, use one hand to perform it, though Gouken can fire two at the same time from different angles.
Zankū Hadōken: Performed by Akuma. An aerial Hadōken meant to surprise and suppress the opponent. He can fire two at once if needed.
Shakunetsu Hadōken: Performed by Ryu and Akuma. A fiery Hadōken capable of scorching the opponent. Ryu's mastered the move well enough to prevent any fatal damage, but Akuma doesn't give a damn.
Gorai Hadōken: Performed by Oni. The mad ogre charges his foul ki with electricity and blasts it at the victim, dealing much damage and shocking the victim to death (or close to it).
Hadōburst: Performed by Sean Matsuda. If the standard Hadōken were a Super Art, this would be it. This move does just one hit, but it's powerful and knocks the opponent across the room. Good move to use if you're being crowded.
Haoh Gadōken: Performed by Dan Hibiki. His most pitiful move is given an Ultra makeover. Dan gathers as much energy as he possibly can (for him) and unleashes it all on his opponent. Not much distance, but it's more damaging than you'd expect, making this move a must for tipping the odds in Dan's favor. Very impressive, but the move tends to blow him away.
Shinkū Hadōken: Performed by Ryu and Sakura Kasugano. A powerful Super Art which sucks the opponent into the surge. Depending on the amount of ki used, up to 5 hits can be drawn from the attack. Sakura, of course, needs more effort to exchange for distance.
Shinkū Tengyo Hadōken: Performed by Sakura Kasugano. An Ultra impressive modification for her, Sakura has finally taken this Super Art and made it her own. She basically shoots her ki at an upward angle, perfect for punishing frequent jumpers.
Messatsu Gō Hadō: Performed by Akuma. A lethal counterpart to the Shinkū Hadōken, this Super Art has the occasional side effect of setting the opponent ablaze.
Tenma Gō Zankū: Performed by Akuma. An aerial Messatsu Gō Hadō. Best used for surprises, this Super Art can kill if needed.
Denjin Hadōken: Performed by Ryu and Gouken. The user gathers as much ki as he can muster and channels his will into a lightning-like nature. The end result is a powerful, 4 hit Super Art that immediately stuns the opponent. Sacrificing power for technique, this is the furthest Ryu has taken the Hadō principle. Gouken is able to knock his opponent back a great distance with this move.
Metsu Hadōken: Performed by Ryu. He channels a bit of the Satsui no Hadō sneaking up on his spirit and releases it, getting 8 hits in. If Ryu is possessed by the evil intent, this Ultra occasionally gains the same paralyzing properties as the Denjin Hadōken.
Messatsu Gō Tenha: Performed by Oni. The demon blasts his vile ki upwards, knocking his foes out of the air with 8 hits.
Messatsu Gō Zanku: Performed by Oni. A lethal move in every sense of the word, Oni launches his ki from the air, giving new meaning to the phrase, "death from above".
Meido Gō Hadō: Performed by Oni. Possibly the most devastating application of this principle. Should he launch it point blank, he will immediately fire another one. The excessive amount of destructive ki then tears the victim apart.
When this style is mentioned, the Hadō principle and the attacks behind it are the first that come to mind. It is very versatile, but you won't gain much prestige at all by abusing it.
(If you must debate me on this and other analyses, please contact me elsewhere. Thank you.)