A Power Chain refers to any chain that pops much more than the standard amount of Puyo at each link. This could involve popping a lot of one color at once, popping two (or more) different colors at once, or both. Due to the way score is calculated, it's possible for a powered-up 10 Chain to out-damage a 12 Chain. Power Chains are advantageous in that not only do they do more damage, but they also resolve much more quickly. Of course, this also makes them crucial for harassment. See Scoring and the Chain Power Table for more technical details.
You should note that some of the following chains do not have an explicit "fixed" form.
Named because it somewhat resembles a real life dam, Dam Stacking (ダム積み) refers to making 3 columns straight across that will pop all at once. Keep extending for a powerful chain, or set it off early for a powerful rush. This is the most obvious way for beginners to make a Power Chain.
Another form that Kuroro seems to have made up. Double Dam has two points where you can Hellfire, or you can set off a shoddy Power 4 from the blues at the bottom. You won't see anyone using this form, including yourself.
Galaxy is an ultra-Double Dam. You won't be making this either, unless you're on TV or something...
Thorns (イバラ) are any powered up 1 Chain. In the hands of a skilled player, Thorns can be deadly since they resolve almost instantaneously. Click here to see a video of this in action.
Napalm (不発弾) refers to the most powerful 1 Chain possible. Not exactly feasible to make, but at the very minimum it does just over 1 rock of garbage. Instantly.
Named after Arle's second voice shout, Hellfire (ヘルファイア) refers to a power 2 Chain. Not as quick as a Thorn, but still very fast and very damaging.
A Death Tower (デスタワー) is a sort of "Tail-Hellfire". It's built in the middle of the board for maximum power.
Twin Tower (ツインプレス) involves making two "towers" at each side of the board pop all at once. This is the basis for some of the above examples.
A Devil Tower (デビルタワー) is a very powerful Hellfire that uses only one side of the board.
Devil Twin Tower
In a Devil Twin Tower (デビルスツインタワー), you now use both sides of the board.
Named after Arle's third shout, Killer Ice (キルアイス) refers to any Power 3 Chain.
Mille-feuille (ミルフィーユ) is another intuitive and common way to make a Hellfire.
L-Murder (L殺し) uses L-Shape as its base.
Haunted House is a Hellfire that requires ghosted Puyo to work.