How can I reduce skill cooldowns?

Diablo 3 cooldowns, by design, are generally longer than Diablo 2 cooldowns. You have the possibility to reduce them slightly with various passive and runes.

Passive Skills that reduces cooldown

Barbarian

• Boon of Bul-Kathos: The cooldown on your Earthquake, Call of the Ancients, and Wrath of the Berserker skills is reduced by 30 seconds

Demon Hunter

• None

Monk

• Beacon of Ytar: Reduces all cooldowns by 15%

Wizard

• Evocation: Reduces all cooldowns by 15%
• Critical Mass: Critical Hits have a chance to reduce the cooldown of your spells by 1 second

Witch Doctor

• Spirit Vessel: Reduces the cooldown of your Horrify, Spirit Walk and Soul Harvest spells by 2 seconds (continue...
• Tribal Rites: The cooldowns of your Fetish Army, Bid Bad Voodoo, and Hex abilities are reduced by 25%

Runes for Active Skills that reduces cooldown

Barbarian

• The Mountain's Call (Earthquake): Removes the Fury cost and reduces the cooldown to 105 seconds (from 120)

Demon Hunter

• None (there are runes that increase the duration of some abilities)

Monk

• Sustained Attack (Seven-Sided Strike): Reduce the cooldown of Seve-Sided Strike by 7 seconds (from 30 seconds)

Witch Doctor

• Desperate Grasp (Grasp of the Dead): Reduces the cooldown of Grasp of the Dead to 6 seconds (from 8)
• Unstable Realm (Mass Confusion): Reduces the cooldown of Mass Confusion to 45 seconds (from 60)
• Devoted Following (Fetish Army): Deacreases the cooldown of Fetish Army to 90 seconds (from 120)

Wizard

• Cold Snap (Frost Nova): Reduces cooldown of Frost Nova to 9 seconds (from 12)
• Force Affinity (Wave of Force): Reduce cooldown to 12 seconds (from 15)
• Perpetuity (Slow Time): Reduces the cooldown of Slow Time to 16 seconds (from 20)

Items that reduces cooldown

There are very few items, all specific to Witch Doctor, that can reduce the cooldown of some skills.

• Zunimassa's Attunement: Requires level 60. Reduce cooldown of Summon Zombie Dogs by 1-7 seconds
• Visage of Giyua: Requires level 60. Reduce cooldown of Summon Zombie Dogs by 1-8 seconds
• Homunculus: Requires level 56. Reduce cooldown of Wall of Zombies by 1-2 seconds
• Uhkapian Serpent: Requires level 60. Reduce cooldown of Wall of Zombies by 1-3 seconds
• Manajuma's Ritual Prize: Requires level 60. Reduce cooldown of Wall of Zombies by 1-3 seconds
• Zunimassa's Ferocity: Requires level 60. Reduce cooldown of Wall of Zombies by 1-3 seconds

Finally, there are passives/runes that prolong the effect of certain abilities.

Skill runes.

Many skills have runes you unlock that reduces the cooldown for said skill.

Some skills and / or runes reduce the cooldown for other skills as well.

There also seems to exist items that reduce cooldown for certain skills but they are said to be rare. See At what point do items that alter specific skills start appearing?.