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Each of the many move classes in CvS2 has its own requirements which must be fulfilled to make it cancelable. Here's a work-in-progress list that i've been meaning to write up for what seems like forever.

Generally speaking, cancelation comes down to two necessary components: a cancelable move and a trigger. Obviously something like lvl3 Shinsho simply can't be canceled no matter what you do. If you've got a potentially cancelable move, it needs a trigger which is usually something hitting the opponent, not necessarily with the move itself.

For example, all you need to make a lvl2 super cancelable is for the opponent to get hit by a super. You can throw a lvl1 projectile then whiff a lvl2 super before the lvl1 projectile connects, and the lvl2 super will become cancelable from when the lvl1 projectile connects onwards. Maybe we can call this remote canceling or proxy canceling.

Some kinds of moves can be kara-canceled for a few frames at the beginning or in some cases they can be whiff canceled throughout the animation.


Uncancelable Moves

1) Dashes are never cancelable
2) Counter Attacks and Counter Rolls are never cancelable
3) Safe Fall and Tactical Recovery are never cancelable


Naturally Whiff Cancelable Moves

1) Rapid fight weak attacks can be whiff canceled into other weak attacks
2) Ground normals during CC can be whiff canceled into specials or supers

Naturally Kara-Cancelable Moves (but not Whiff Cancelable)

1) All normal moves can be kara-canceled into specials or supers
2) LP+LK roll can be kara-canceled into specials or supers


C-Groove Lvl2 Cancel Rules

1) Lvl2 supers can be canceled into specials and supers
2) Non-throw lvl2 supers normally become cancelable when they connect
3) Lvl2 super cancelability can also be triggered by another super connecting after the lvl2 super is initiated


A-Groove Custom Combo Rules

1) Connected attacks can be canceled into normals, specials, or supers during CC
2) Normals can be whiff canceled into specials or supers during CC
3) Air command normals can be whiff canceled into specials or supers during CC
4) Airborne specials can be whiff canceled into specials or supers during CC
5) Nearly all moves can be proxy/remote canceled using projectiles


Throw Rules

1) Normal throws are generally never cancelable
2) Recovery periods of many command throws are cancelable in situations where special/super moves can be canceled
3) Many cancelable command throws are actually missing the required trigger, such as Benimaru's and Morrigan's command throws
4) Throws are never cancelable while the actual grab portion is in progress

Certain command throws are not cancelable on their own because most throw hits don't fulfill/satisfy the cancelability trigger requirement. However, if a projectile hits the opponent after the command throw is initiated, the command throw becomes cancelable. For whatever reason, Rolento's lvl2 Take No Prisoner falls under this behavior category, becoming cancelable after a lvl1 Steel Rain connects.


CvS2EO P-Groove Cancel Rules

1) Special moves can be canceled into supers
2) Special moves normally become cancelable when they connect
3) Special move cancelability can also be triggered by a projectile connecting after the special is initiated


Notes and Exceptions:

1) LP+LK roll, LP+LK dodge, and teleport specials can't be remote/proxy canceled during CC's or using CvS2EO P-Groove
2) LP+LK dodge can only be canceled directly into a pre-determined punck or kick, one of which can then be kara-canceled

Hah, wayyyy off topic, but that lv1/lv2 thing made me laugh hard, cuz you could do that in Killer Instinct.
On SNES: Have Thunder do a combo ending in (C)B,F+3 (3 = Fierce), then throw his juggle fireball and jump forward with an air move. When the fireball hit, it would allow you to cancel out of the air move into your air-double and juggle them again, as if the air move had hit the falling opponent (which is impossible due to KI's juggle rules).
On N64: If Glacius threw a FB (multi-hit super fireball is easier since the recovery is shorter), then did his super command throw, when the fireball hit it would trigger the command throw from anywhere on the screen, resulting in a magic throw. This worked even if the FB was blocked or hit in the air, since the command grab was unblockable and would go off on hit or block. This was actually helpful in making him god-tier, although nobody played that game enough for it to have real tiers.

Mike Z