When are Archons useful?

I've played about 50 games and haven't built/seen a single Archon. When should they be used?

One possible use case is when you're massing Dark Templars, and then find that your opponent has detection everywhere.

• When your high templar run out of energy in a battle, morph them into archons to gain some extra firepower for the fight .
• They do bonus versus biological units, which means every zerg unit and terran infantry.
• EMP only removes 100 shield, so you can use them vs terran bio, even if they have ghosts.
• They do well vs mutalisks, zerglings, and zealots in fights thanks to their splash damage...but they are not so good at stopping mutalisk harassment.
• They can act as effective tanks for your other units, preventing units such as ultralisks from actually getting to your immortals while the immortals dish out heavy damage.
• Their splash one hits broodlings, so they can help out vs broodlords as well, even if they don't get to hit the actual broodlord.
• You can fire at your own to charge your void rays...the shields will regen

In general though, your high templar are going to be more effective vs most things, so you'll usually only morph them after storming, but try them out in some of the scenarios I listed, they are actually fairly powerful.

There's also the Archon toilet, wherein you throw 5-6 Archons in a Vortex along with your opponent's army. Since Archons do splash damage, they'll do incredible damage when they pop out of the Vortex.

Though you can probably only pull this off in a team game, since it requires both a Mothership and a lot of Archons.