Kormac the Templar

Strengths

• Good support character for higher difficulties, ranged classes, or while initially learning the game. Can heal and taunt from the player when they are at low health.
• Decent Tank, as he can be equipped with one handed weapons and a shield in addition to rings and amulet.
• Can provide good DPS through the use of items that give "Thorns" type damage on hit, as he will charge into the thick of combat and be hit by packs of enemies.
• Level 20 "Inspire" ability helps with resource regeneration for the player, leading to more opportunities for ability use

Weaknesses

• Susceptible to being surrounded and killed fairly easily if not geared properly. His charge in and hack style gets him killed a lot by high difficulty elites.
• Not a particularly good direct damage dealer

Suggested follower for: Demon Hunter, Wizard, Witch Doctor, though he is a very useful follower for any class at more difficult stages.

Suggested Gear Stats: Vitality, Strength, "Thorns" type damage on being struck in melee

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PLEASE NOTE: Follower stats are increased by a 2.5x multiplier on the 4 base stats, as denoted in this post. Therefore, it is worthwhile to give followers items that increase these stats primarily.

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Lyndon the Scoundrel

Strengths

• Good ranged support character for melee classes, has decent crowd control ability
• Offensively focused, can deal more direct damage than the Templar and Enchantress
• Good survival ability, high dexterity boosts his dodge chance and helps him avoid taking damage. Level 15 "Vanish" ability allows him to drop aggro and heal himself.
• Can provide a boost to critical hits using either of his Level 25 abilites "Anatomy" or "Hysteria" depending on preference
• Witty and humorous, making his dialogue more interesting than other followers

Weaknesses

• Not extremely durable if he gets cornered
• Crowd control abilities are inferior to those of the classes he is ideally supporting
• Like the Enchantress, is prone to pulling groups before a player is ready

Suggested follower for: Barbarian at early difficulties where Templar healing is not necessary, Monk at all difficulties.

Suggested Gear Stats: Dexterity, Vitality, +Damage, +AtkSpd, Crit%

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Eirena the Enchantress

Strengths

• Good ranged support character for melee classes, has excellent crowd control ability
• Good balance of support spells and damage dealing
• Can buff the attack speed of the hero
• Her Charm ability even works on elites (non-boss), which will completely incapacitate them for a short time or turn them against their allies. Very helpful on high difficulties.
• High intelligence allows good mitigation of ranged attacks

Weaknesses

• Not durable, but can generally get out of trouble with excellent crowd control ability
• Damage is inferior to Scoundrel, and can also be inferior to a properly geared Templar
• Like the Scoundrel, will pull sometimes before player is ready

Suggested follower for: Barbarian at early difficulties where Templar healing is not necessary, Monk at all difficulties, Witch Doctor at any difficulty.

Suggested Gear Stats: Intelligence, Vitality, +Damage, +AtkSpd

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Basically you should pick the follower to support your playstyle. I personally prefer to have the Templar following me just about everywhere as I can count on him for an emergency heal and taunt when I get in trouble, he also provides increased resource regeneration so I can use my skills more often. However, there are obvious benefits at lower difficulties to use the Scoundrel, where a tank type may not be as necessary and the direct DPS increase helps get through mobs quicker. The Enchantress can also be a good choice due to her CC ability in late difficulties where you don't want to get overwhelmed by numbers.

THIS GUIDE IS CURRENT AS OF PATCH 2.0/REAPER OF SOULS

Check out this post on Treasure Creatures.

Of note is the following graph that shows some interesting trends for the different goblin types.

It looks like the loot distribution depends on the name, not the color. Take this data with a grain of salt though, the sample size was fairly low.