I meet a lot of players that don't know about this, so I'm finally going to do a big long write-up to try to cover all the basics of clickies, especially instant ones. Please feel free to add any info I have missed. Perhaps I'll do a second draft with further information and revisions suggested by other posters.
Summary of purposes of instant-click items:
1. Reset global cooldown, eliminating the delay between casting spells. It’s like haste for casters!
2. Clicky junk buffs protect other more valuable buffs from dispels, especially raid mob AE dispels.
3. Hey, mana-free buff!
1. Reset global cooldown
Ordinarily, you have to wait approximately 1.5 seconds after finishing a spell to start another spell. However, the game lets you use clicky items like a
Pegasus Feather Cloak (6-second cast time) immediately after casting a spell; and the game lets you cast a spell immediately after a clicky item’s cast time concludes. Therefore, if you click an item with an instant cast time immediately after finishing a spell, you may immediately begin casting another spell. It’s classic!
CAVEAT: if you want to chain-cast the same spell, it has to be in spell gem slot 1. Slots 2-8 won’t let you repeat the same spell over and over. However, you can go Spell 2 - clicky - Spell 3 - clicky - Spell 2 and so on. On a wizard, you can do this with a nuke and Concussion to maximize your damage rate.
CAVEAT: certain spells have their own cooldown, separate from the global spell cooldown, which cannot be circumvented. Harvest and Theft of Thought are examples.
Hotkey it: there’s no need to click an item with your mouse, as you can hotkey it by holding left click on the item (or rather, on the inventory slot).
Notable applications of clicky GCD reduction:
• Crowd control, such as root, stun, mesmerize, and charm. Resetting global cooldown lets you pop off more spells faster, which can be critical in crowd-control situations or to regain control when charm breaks. Note that if you want to chain stun, you will need more than one stun spell memorized, as most stuns have a built-in cooldown longer than global cooldown.
• Cannibalize (shamans). Quickly canni-clicky-canni etc, then sit and regen. A less efficient but less concentration-intensive alternative to canni-dancing. Unfortunately, Cannibalize is one of those spells with a built-in cooldown; you have to wait about half a second to recast it even if you use a clicky. Clicky canni is still faster than canni with no clicky, though. You can also alternate two different cannibalize spells to get around this.
• Quadding - It’s helpful (though not required) to flux staff your quad in between nukes to allow yourself to cast them earlier and get back to medding sooner. Flux it up!
• Chain nuking with a nuke in Spell Gem 1. Great when the target is snared, rooted, or firmly aggroed.
• Buffing. For example, as a shaman: target Soandso, cast AC buff, clicky, cast agility buff, clicky, cast dexterity buff, clicky, cast strength buff, clicky, cast stamina buff, clicky, cast regen, clicky, cast haste. Sit; or target the next person and repeat. That saved about 9 seconds.
• Note that bards do not experience global cooldown.
2. Clicky junk buffs
Some mobs (or players, if PvP) dispel you. However, the dispel of a raid mob's AE is different from those cast by regular mobs.
a. When a regular mob, such as a goblin, casts a dispel, it uses “counters” to determine which buff to remove. This means they can skip buffs and dispel seemingly at random. However, if you place junk buffs first in your buff stack, they at least have a chance to be dispelled first, so you have a greater chance of keeping your more valuable buffs.
b. When a raid mob procs a dispel AE, such as Nagafen or Vox, it is guaranteed to remove your first buff. A clicky junk buff can be used to eat this dispel, then immediately reapplied. This will protect more valuable buffs from dispels.
As a side note, it is ideal to apply less-important buffs before more-important buffs for the same reason. Spirit of Wolf, Clarity, and big HP buffs like Aegolism or Protection of the Glades should be applied after a few other buffs so they are less likely to be dispelled. You can even cast unnecessary buffs like Resist Disease or vision buffs as junk buffs.
Even non-instant clicky junk buffs can be better than none, such as the 20% haste from Eyepatch of Plunder. This can be reapplied mid-fight if dispelled.
3. The buff itself
Some instant-cast buffs are actually desirable for the buff.
• As a wizard, I often cast Elemental Armor, a self-only +30 fire resist, +30 cold resist buff. Now that I have Sage’s Pantaloons (Velious/Thurgadin), I don’t have to cast it anymore. I have it up all the time. You never know when you'll get fire/cold nuked!
• On my cleric, I have a Fright Forged Helm, which has instant-cast Deadeye, which grants infravision and see invisible. It’s nice to have infravision on an Erudite or a Human; and it’s a nice perk to have see-invis on a cleric. Both would otherwise go without.
• Technically the Shrunken Goblin Skull Earring should make you hit harder, but it’s probably not much. I believe most people want it to reset GCD or eat dispels.
I hope this has been informative. Please feel free to make corrections and clarifications or add any info I have missed.