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.

Sunward Lightbringer (Paladin only)

Lightbringer Faceguard Token to buy this drops from Archimonde in Hjyal Summit or you can buy Vengeful Gladiator's Lamellar Helm from Kezzik the Striker in Area 52 for 1000 Honor Points or get Crown of Empowered Fate from Essence of Anger in the Black Temple.
Lightbringer Pauldrons Token to buy this drops from Mother Sharaz in Black Temple or you can buy Vengeful Gladiator's Lamellar Shoulders from Kezzik the Striker in Area 52 for 750 Honor Points.
Heroes' Redemption Tunic >Drops from Archavon 10 or buy with Chestguard of the Lost Conqueror token that drops from Gluth in Naxx 10 or you can buy it in Dalaran.
Tabard of the Shattered Sun Requires Exalted with Shattered Sun Offensive
Heroes' Redemption Gloves> Drops from Archavon or buy with Gloves of the Lost Conqueror token, which drops from Satharion in the Obsidian Sanctum or you can buy the token in Dalaran.
Tainted Girdle of Mending > Drops from Patchwerk in Naxx 10
Heroes' Redemption Greaves:> Drops from Archavon 10 or buy with token that drops from Thadius in Nax 10.
Sabatons of Deathlike Gloom Drops from Gothik the Harvester in Naxx 10
The Willbreaker Drops from Keli'dan the Breaker in The Blood Furnace heroic
Sunward Crest Requires exalted with Shattered Sun Offensive

Details here.

Emerald Dragon's Call

My dwarf paladin lucked out and got the sword Dragon's Call today, and I happened to have gotten a good deal on an Emerald Shield at the Auction House yesterday, so I decided to try to come up with an outfit using both.

Bog Pauldrons Drops from the rare mob the Bog Lurker in Zangarmarsh.  It's BOE, so your best bet may be the Auction House.
Emerald Breastplate Green BOE
Emerald Vambraces Green BOE
Emerald Gauntlets Green BOE
Emerald Girdle Green BOE
Greaves of Pacification Buy for Justice Points in Shattrath
Emerald Sabatons Green BOE
Dragon's Call Rare drop from the Shade of Eranikus in the Sunken Temple.  Chance on hit to summon an Emerald Dragon Whelp.
Emerald Shield Green BOE
Tabard of the Wildhammer Clan Alliance only

Details here.


8/2/12 edit:


Here is the completed set on my paladin.  I made a few changes from the set above.

Jade Warrior Pauldrons Quest reward from Hellfire Ramparts.  Same model and color as the Emerald Pauldrons.
Chimaerascale Legplates Blue BOE.  I lucked out and got these as a drop.
Stylish Black Shirt

If I only had a Tiny Emerald Whelpling pet, I'd be complete.

Details here.

Also, note that blacksmiths with Cenarion Circle rep (not Cenarion Expedition) can craft the Ironvine Breastplate, Belt, and Gloves, which are identical in appearance to the corresponding Emerald set pieces.