What goats can I unlock?

Solution 1:

There are

• Angel Goat - Gives a halo and increases jump skills.
• Devil Goat - Gives devil powers as an R toggle ability.
• Ripped Goat - Increases attack strength.
• Tall Goat - Is tall
• Feathered Goat - Moves faster
• Giant Goat - Is giant
• Robot Goat - Is a robot
• Space Goat - Spaceeeee. (Also a pain to try and play as.)

In addition to these, there are mutators that, while they may change only a little visual appearance of your goat, they give you additional R power. These include:

• Pitcher Goat - R ability to 'throw' balls.
• Jetpack Goat - R toggle ability to fly!
• Blue Streak - Can charge up spin attacks like sonic.
• Yoshi Goat - Can lick objects, then press r to turn them into bombs.
• Goat Queen - R ability to summon peasants.
• Goatborn - R ability to fus-ro-dah!

As far as I know, only Angel Goat, Devil Goat, Ripped Goat, Pitcher Goat, and Jetpack Goat can be used in a non-custom game. The others can be used in custom games.

Unlocking Goats:

Goats that are unlocked through collecting a certain number of goat trophies:

• Tall Goat
• Feathered Goat
• Giant Goat
• Space Goat - Collect all trophies.

Goats that are unlocked by touching certain objects in game.

• Jetpack Goat - At construction site, on 2nd highest level.
• Pitcher Goat - At batting cage next to spawn.
• Goat Queen - Throne in palace reached by climbing goat tower at spawn and going in top door.

Goats that are unlocked by completing certain objectives in game.

• Angel Goat - No rag dolling pedestrians for a certain time.
• Devil Goat - Bring 5 sacrifices to the Goatacle.
• Ripped Goat - Defeat all goats in the goat fighting ring.

There may be more, so if others are found, feel free to edit this answer and add them to the list.

Update: 1.1 Added the following new goats

Uncle Goat:

• Unlock by walking into the room in the building next to the skate park. There will be a large alien-ish container that has it.

Classy Goat:

• Get 5 golden goat trophies.

Shopping Goat:

• Get 20 golden goat trophies.

Builder Goat:

• Find one of the 3 minecraft blocks.
• There is a cobblestone block at the graveyard, past the wind turbines.
• There is a dirt block up the hill next to the skate park, near some trees, to the right of the 3 boulders of death.
• There is a wooden block by the thickest tree closest to the shore, across the water from the theme park.

DeadGoa7:

• Go near/lick DeadMau5. He will be at the top of the skyscraper. You can get there through the lift inside, at the bottom.

Repulsive Goat:

• Enter the sewer. It is at water level, next to the bridge.

Tornado Goat:

• Get the tornado sculpture on top of the middle wind turbine, and bring it to the wind altar, located between the skate park and the dam.

Double Jump:

• Unlocked by default

Rocket Skate Goat:

• Get 30 golden goat trophies.

Hitchhiker Goat:

• Bring a towel with the number 42 on it to the crashed UFO near the dam. You can get the towel next to the pool, at the second highest roof party of the skyscraper.

Solution 2:

As far as I've seen you can become Goat king and unlock the "Devil Goat". I've not seen any other unlocks.

How to Become Goat King [Easter Egg]

As the diabolical Goat King, you can summon dead goats with the push of a button. Nice, right?

Step 1

Near where your goat spawns, there’s a strange spiral tower in the corner of the fenced-in space. One goat is standing watch on the ground, while another sits inside the door half-way up. Climb the spiral stair-case and enter the top door for find a surprising congregation.

Step 2

Welcome to your throne room! At the top of the tower, entering the highest door will take the goat into his palace. Walk forward, and the goats will bow to you. As it should be. Sit (or stand, like a goat) on the devilish looking throne and you’ll earn all the power of a Goat King! So, what were all those powers again?

Step 3

Standing on the throne causes plumes of smoke and fire to raise up and engulf your goat, transforming it and teleporting it back to the original spawn point.

Skills

As a Goat King (with a spooky skull mask) you can make it rain goats whenever you like! Just press the action button [Default: R] to drop rag-doll goats from the sky in infinite quantities. Enjoy!

How to Unlock Devil Goat [Easter Egg]

Step 1

A giant red-glowing Pentagram exists at the corner of town. Find the community pool in the suburban area where two water-slides are positioned on the hill. From the bottom of the hill, while looking up at the slides, you should see a large electrical tower to the far left. Right next to the electrical tower, you’ll find the Pentagram. If you’re having trouble spotting it, try grabbing a jet-pack, or let a car slam into the goat and fly into the sky for a bird’s eye view.

Step 2

To unlock the powers of the Devil Goat, you’ll need to bring 5 bodies to the Pentagram. Latch your tongue onto a human and leave them on the Satanic circle. Make sure to place the bodies on each of the five points of the star. That’s probably the right way to go. [Unconfirmed]
This can also be done with goats. If you’ve unlocked the power to summon goats, you can use that to easily complete the Devil Goat challenge. Check out our guide on how to become the Goat King for more details.

Step 3

With all 5 bodies, you should instantly transform into the demonic Devil Goat! After the bodies are sucked into a ball and explore, that is.

Skills

As a Devil Goat, you can fly! How? Summon a Black Hole [Default: R] then go into rag-doll mode [Default: Q] and you’ll instantly freak out. Beware, this is an easy way to explode into the environment and die instantly.
While flying, go into slow-motion [Default: F] for best and most hilarious results.
The other, and slightly safer, ability of the Devil Goat is to summon Black Hole energy [Default: R] which sucks up any rag-dolls nearby. Kind of like a souped-up tongue, you can drag these unfortunate objects / people where ever you want.