Cloth (no spirit) : Mage, Warlock, and on some occasions Shadow Priest.
Example : Shadowblaze Robes
Cloth (with spirit) : Priest.
Example: Robes of the Burning Acolyte
Leather with Agility : Rogue, Feral Druid ( Enhancement Shaman / Hunter up until level 40 ).
Example: Sark of the Unwatched
Leather with Intellect / Spirit : Balance or Restoration Druid ( Elemental / Restoration Shaman up until level 40 ).
Example: Scorched Wormling Vest
Strength Mail : Paladin / Warrior armor up until level 40.
Example: Mail Combat Armor
Intellect Mail : Restoration / Elemental Shaman ( Holy Paladin level 1-40 although rare to find at lower levels )
Example: Circuit Design Breastplate
Agility Mail : Enhancement Shaman / Hunter level 40+
Example: Voltage Source Chestguard
Strength Plate ( With Haste / Critical / Hit / Expertise / Mastery ) : Level 40+ Fury or Arms Warrior, Retribution Paladin, Unholy or Frost Death Knight.
Example: Battleplate of Ancient Kings
Strength Plate ( With Dodge / Parry / Mastery ) : Blood Death Knight, Protection Paladin and Protection Warrior.
Example: Battleplate of the Apocalypse
On some occasions you will find gear that looks as though it would work for Damage Dealers or Tanks, I/E the example by Cogs below, Here you would have to look at the socket bonus, if its a combat stat it's probably damage if its avoidance or stamina then it is more than likely meant for a tank; although it can be used as an upgrade for a Damage Dealer in a situation where nothing better is available.
Example: Dragon Bone Warhelm
Intellect Plate : The only class that benefits from this is Holy Paladin, as of this time there are no other actual classes or specs that benefit from this.
Example: Breastplate of Avenging Flame
Intellect Trinkets with effects that start to proceed into effect via damaging effects are shared between : Shadow Priest, Mage, Warlock, Balance Druid, and Elemental Shaman.
Example: Bell of Enraging Resonance
Intellect Trinkets with effects that proceed into effect via healing spells or effects are shared between : Restoration Shaman, Holy Paladin, Holy and Discipline Priest, and Restoration Druid.
Example: Fall of Mortality
Strength Trinkets with effects that proceed into effect via damage are generally for damage dealing plate classes.
Example: Crushing Weight
Agility Trinkets are used for both Feral Damage Dealers and Tanks, along with Rogues, as well as Hunters and Enhancement Shamans.
Example: Essence of the Cyclone
Most tanking trinkets have dodge or parry on them, with mastery effects or parry or dodge. Also many tanking trinkets have an effect that if your below a certain % of health that it will go into effect. Druids have no use for parry so those types of trinkets will be for Death Knights, Paladin and Warrior. Dodge Trinkets would be shared between all types of tanks.
Example: Gift of the Greatfather or Symbiotic Worm or Throngus's Finger
Look in the post below for a URL of a chart and a more streamlined light reading version.