Go to the store and buy the following characters when you have the earned the specified amount of coins. As of 1.4.1 there are seven characters to choose from.

Guy Dangerous
Default character.

Scarlett Fox
Earn 10,000 coins.

Barry Bones
Earn 10,000 coins.

Karma Lee
Earn 25,000 coins.

Montana Smith
Earn 25,000 coins.

Francisco Montoya
Earn 25,000 coins.

Zack Wonder
Earn 25,000 coins.