Righteous Crystal

Brighthelm of Justice:  Drops from Hydross the Unstable in Serpentshrine Caverns.
Pauldrons of the Argent Sentinel:  Drops from Morogrim Tidewalker in Serpentshrine Caverns.
Justicar Chestguard:  Paladin only.  The token for this drops from Magtheridon.  There are several other similar chest pieces that could be used by any plate wearer.
Gauntlets of the Righteous:  Dropped by Warchief Kargath Bladefist in Shattered Halls.
Girdle of Valorous Deeds:  Dropped by Aeonus in Heroic Black Morass.
Legplates of the Righteous:  Dropped by Aeonus in the Black Morass.
Boots of the Righteous Path:  Dropped by Warchief Kargath Bladefist in Heroic Shattered Halls.
Icy Cloak:  Crafted by Tailors.  There are a number of other cloaks with the same appearance.
Bloodmaw Magus Blade:  Dropped in Gruul's Lair.
Aldori Legacy Defender:  Dropped in Gruul's Lair.

Details here.

Corrupted Mooncloth

Vengeful Gladiator's Mooncloth Hood Priest-only PvP reward.
Merciless Gladiator's Mooncloth Mantle Priest-only PvP reward.  The token to buy it drops from Void Weaver in The Eye.  ** Update 11/22/2013:  Not sure when this changed, but you can now buy this from Kezzik the Striker in Area 52 in Netherstorm for 750 Honor.  **
Raiments of the Corrupted Drops in Ulduar 10
Binding of the Dragon Matriarch Drops in Ulduar 10
Pulsar Gloves Drops in Ulduar 10
Royal Boots Green BOE
Tower of the Mouldering Corpse Drops in the Forge of Souls
Deathchill Cloak Made by Tailors.  There are a few other cloaks with the same appearance.

Details here.

Icy Mooncloth

Here's a set based around the Mooncloth Robes for a Frost Mage or healy Priest.

Royal Headband Green BOE
Regal Mantle Green BOE
Mooncloth Robe Made by tailors
Ebonweave Gloves Made by tailors.  They are long enough that most bracers shouldn't show.
Mindfire Waistband Drops in the Blood Furnace
Staff of the Unknown Road Quest reward from Zul'Farrak
Regal Boots Green BOE

Alternate version

Underworld Mantle Drops in Ulduar 10 normal
Grand Magister's Staff of Torrents Drops in Sunwell Plateau

Alternate Shoulders

Khadgar's Shoulderpads of Triumph Alliance Mage Tier 9

Merciless Gladiator's Mooncloth Mantle Priest-only PvP reward.  The token to buy this drops from Void Reaver in the Eye.

Sanctified Crimson Acolyte Mantle Priest Tier 10

All details here.