What are colored coins? What exactly are colored coins? I've tried understanding, but I don't quite get it yet . . . Do any examples exist?
Colored coins are a method to track the origin of bitcoins, so that a certain set of coins can be set aside and conserved, allowing a party to acknowledge them in various ways. Such coins can be used to represent arbitrary digital tokens, such as stocks, bonds, smart property and so on.

The colored coins protocol is decentralized just like Bitcoin, but the current effort to develop an implementation is done under the BitcoinX project (tentative name), which also aims to provide some related services.

As this is still under development, you will not find any existing examples.

You can read more about it in Overview of colored coins (work in progress).