Diablo 3 Gemming Guide submitted by Galaedria.

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Regardless of your jeweler’s skill level, some gems are better than others for different classes or followers, however, the situation may also change depending on your play-style and whether you’re playing in a group or soloing.
Gem Colors

Helm Sockets

The gem options available are more about utility than boosting output. In general, the amethyst gem with its +life bonus will probably be the most solid choice throughout the game. The ruby gem with +experience may be helpful during levelling while the topaz gem may increase your chance of finding good gear upgrades with its +magic find bonus.

Suggestion: Use amethyst gems in helm sockets to increase survival.

Weapon Sockets

The weapon socket (on either main hand or off-hand items) options are rather interesting. For melee classes and followers (i.e. barbarian, monk and templar), the thorns bonus from the topaz gem should increase damage output the most. For ranged classes and followers (demon hunter, witch doctor, wizard, enchantress and scoundrel), getting hit by melee is generally to be avoided, so the straight damage boost from rubies may be better. For anyone focussing on improving survival the amethyst with its +life/hit bonus may be the gem of choice.

Suggestions: For most builds, an emerald is your best bet end game as it vastly increases your DPS with critical damage. For lower levels, a ruby is better because you may not have high crit yet.

Other Sockets

In any other sockets (amulets, rings, legs, belt, bracers), characters will either be stacking their primary stat, or amethysts (+vitality) for increasing survival. This means that barbarians and templars want rubies (+strength); monks, demon hunters and scoundrels want emeralds (+dexterity), and witch doctors, wizards and enchantresses want topaz (+intelligence).

Suggestion: For survival builds, use amethysts. Use rubies for strength, emeralds for dexterity and topaz for intelligence.