Hearthpwn

Peak NA Legend Rank: 1315 (Season 15)

General Strategy:

Race through your deck with Power Word: Shield, Harrison Jones, Northshire Cleric, and Acolyte of Pain (comboed with Wild Pyromancer, Holy Nova, and Circle of Healing).  Keep the board clear with AoE: Lightbomb, Holy Nova, Auchenai Soulpriest + Circle of Healing, Wild Pyromancer, and Doomsayer.  Then combo Stormwind Knight / Gnomeregan Infantry with Power Word: Shield / Velen's Chosen / Divine Spirit + Inner Fire for the win.

The entire deck sticks very close to this premise.  Alexstrasza can help you move your opponent into combo range.  Emperor Thaurissan enables larger combos.  Deathlord's help you survive longer, while providing a solid alternative target for Inner Fire.  Silence is primarily there to move taunts out of the way for your combo.  Finally, a Shadow Word: Death rounds out the decklist with some cheap, but situational, removal.

Mulligan Guide:

This is roughly what I do, although with this deck more than some others, the other cards in your hand can dictate what you keep.  Notice that you generally do not want to keep the combo pieces in hand.  You'd rather get your draw engine going.

Always Keep: Circle of Healing, Power Word: Shield, Northshire Cleric, Wild Pyromancer, Acolyte of Pain, Deathlord
Sometimes Keep:
Velen's Chosen:  With a couple other 3 mana cost or less minions
Auchenai Soulpriest, Doomsayer and Holy Nova: Against Hunter, Mage, Paladin, Shaman, Warlock
Harrison Jones: Rogue, Paladin, Warrior
Emperor Thaurissan: Priest, Warrior

Matchups:

From rank 5 one star to legend, I had a 61% win rate.  I've listed my records in individual matchups from most statistically favorable to least.  Other is the aggregation of matchups I faced fewer than 5 times.  I've included links to some very low quality videos of me manning the deck in these matchups, which could be valuable for seeing how the deck functions.

Aggro Paladin (6-1, 86%): Focus on survival.  You have lots of AoE that should carry you through, and don't go too far out of your way to draw cards, since he'll probably have Divine Favor.
Handlock (6-1, 86%): Handlock is slow enough that you have plenty of time to put your combo pieces together, maybe even on a Deathlord.  Lightbomb is incredibly strong here.  The only real danger is that your opponent gets too many taunts down for you to get through, so be very careful with Silence (even though it is very tempting to use it on those Twilight Drakes)
Midrange Paladin (6-1, 86%, video is match to make legend): AoE wins this matchup.
Face Hunter (9-3, 75%, includes hybrid, video is against Chakki): Focus on survival and if you have some AoE, prefer healing yourself to playing a minion from turn 5 or so onward.  If you believe they don't have silence, don't be afraid to buff up Deathlords with Divine Spirit for extra protection.
Control Warrior (6-3, 67%): Alexstrasza is pretty key here.  Do what you have to to kill Armorsmiths early, maybe even silencing them, as they are the main way that you can lose.  Otherwise you'll have plenty of time to find your combo.
Tempo Mage (8-5, 62%): Focus on survival, including Silence on Flamewakers that you can't kill.  Play Doomsayer into Mirror Entity for a board clear.  Look for every opportunity to heal yourself, since these decks pack a lot of burn, but they also seldom run hard removal or silence, so you can do a non-lethal Inner Fire combo.
Other (14-9, 61%, video is a turn 5 win)
Midrange Hunter (7-5, 58%): Like Face Hunter, keeping your life up is pretty key, but you'll want to hold some cards back for a finishing combo.
Midrange Druid (6-9, 40%, video contains 56/56 Deathlord):  It just always seems to be awkward destroying their minions, taking far too many cards.  On the plus side, you'll often have time to put together a good Circle of Healing + Northshire Cleric combo
Patron Warrior (3-5, 38%): Save Harrison Jones for a Death's Bite to block a strong combo.  Make sure you have AoE to clean up his combo and keep your health high.  When I win, its usually because I just outlast him.  They can usually find their combo before you can, so you have to ride it out.
Zoo (1-5, 17%): AoE will keep you alive for a while, but eventually Life Tap takes away your card advantage from being efficient.  In the meantime its tough to split your Silences between the taunts and the times you really need it to clear.  There is too much pressure to wait a long time, but Circle of Healing + Northshire Cleric combo can help you find your combo fast.

Selected Card Explanations:

Inner Fire, Divine Spirit, Gnomeregan Infantry, and Stormwind Knight:  These are your combo pieces and you generally should not be using them outside of that context unless you have another game winning combination in your hand.  The exception is against aggro (not including zoo) where you can probably just outlast them and don't need the combo to win.  Also a note on having one Gnomeregan Infantry and one Stormwind Knight.  Sometimes you really need the one mana, sometimes the one health, and occasionally even the taunt.  By the time you are ready to combo, you're likely to have both and can choose which one works best.

Doomsayer:  This is an odd one, but it can be a huge tempo boost.  If you play it when your opponent has one minion down, you can hopefully kill their minion, and ensure a clear board for the start of your turn.  Now often that won't work, but if they kill it directly, that's at least 7 damage absorbed, often more.  If they silence it, they leave an excellent buff target on the board, especially with Inner Fire.  Also, it can be played into a Mirror Entity for a board clear, which is pretty nifty.

Northshire Cleric:  This card is very key to the deck and needs to get you some draws.  It's generally not a good idea to drop it without a clear plan for how to get draws.  Against aggro it can be helpful to play it early.  Sometimes you can run one out early with a Power Word: Shield if it seems like your opponent will have a hard time killing it.  When it doubt, hold it.  Keep track of how many cards are in your hand and try to avoid having them burned.  On the other hand, it's generally better to draw 3 cards and have 1 burned than not draw any at all.  Having cards burned usually isn't that bad (though losing a Divine Spirit can be rough).  Finally, Circle of Healing turns can take a long time and a lot of planning.  There is definitely a danger of running out of time, so think quickly but carefully.

Harrison Jones:  Potential card draw and a decent sized body.  This deck does a good job of clearing the opponent's minions, but without many minions of your own, weapons can eat into your health pretty fast.  Destroying a weapon can help edge out some games.  Even in a meta not dominated by weapon classes, he can be worth his slot.

Silence:  This is mostly for removing taunts for your finishing combo, so be careful using it earlier in the game if you anticipate seeing more taunts later.  Keep in mind that it can be used to silence Auchenai Soulpriest, Wild Pyromancer, and Deathlord, but this is rarely necessary.

Power Word: Shield:  Early in the game, don't save this for your combo.  Use it to get some board presence and find your draw engine.  Once you get some card draw going and have a decent sized hand (about 8 or more cards) you should hold it for the game winner.  Also, if you can see the game winning combo, but are just a card short, it may be worth holding in that case too.

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Write questions or suggestions in the comments.  For anyone who gives this deck a shot, let me know how it goes and good luck!

Thank you to XRBlackWolf for help in deck development.

Deck in Action:

Check out my Twitch channel, www.twitch.tv/crusherhs.  Here is an example of me playing the deck: http://www.twitch.tv/crusherhs/v/7456065

Golden Wisp Podcast reviews Crusher Combo Priest in its Decklist of the Week segment.  There's some good discussion about card choices and strategy in the deck.  Check it out for this and other Hearthstone news.

Noxious plays the deck on his stream having some good success and thoroughly enjoying the deck, proclaiming that it has the most beautiful lethals.