Take a look at this nice attempt at redesigning the US Dollar by the Dowling-Duncan firm. I quote part of their interesting design brief below.

We wanted a concept behind the imagery so that the image directly relates to the value of each note. We also wanted the notes to be educational, not only for those living in America but visitors as well. [e.g. $1 – The first African American president; $10 – The bill of rights, the first 10 amendments to the US Constitution; $100 – The first 100 days of President Franklin Roosevelt.]

We have kept the width the same as the existing dollars. However we have changed the size of the note so that the one dollar is shorter and the 100 dollar is the longest. When stacked on top of each other it is easy to see how much money you have. It also makes it easier for the visually impaired to distinguish between notes.