The purpose of money is to provide a uniform method for valuing things. It doesn't matter whether I have a crisp new $1 bill in my pocket, an old dollar bill, four quarters, or even a check made out to me for a $1. They all have the same value. This currency system allows us great freedom to buy and sell things and services.
Despite the great flexibility that money permits us, people have trouble treating every dollar the same as every other dollar. Here are two examples.
First, sociologist Viviana Zelizer in her fantastic book The Social Meaning of Money has done an extensive analysis of the way that people use money. One thing that becomes clear quickly is that people really do create different types of money to help them organize their lives. As a simple example, people treat birthday money differently than other money. For example, if a relative gives you $25 for your birthday, you are likely to spend it on something nice for yourself rather than on bills, even though the gift money is part of your total pile of money once it has been given to you. That is, we keep the money psychologically separate.
One way to see this idea of different types of money is in gambling behavior. There is a phenomenon that arises in research on gambling called the "house money effect." Basically, people get more risky in their bets when gambling after they have won a bit. The idea is that the money that they have won isn't really theirs. They are gambling with the house's money. Somehow, that money is less valuable, and so people are more willing to risk it.
The second example ties the value of money to our motivational system as well. A new study by Adam Alter and Danny Oppenheimer in the October, 2008 issue of Psychonomic Bulletin & Review, looked at how the ease of thinking about money influences the value of money. This ease of thinking is usually called fluency. Alter and Oppenheimer suggested that being more fluent with a type of money would make that money seem more valuable.