I like a controlled scrappy look, so I buy fat quarters to allow me to blend lots of fabrics, or to give lots of variety. If I'm making a small project, a fat quarter can be a good amount (for example, 4-6 fat quarters plus 1 yard of a constant can make a nice baby quilt). Bags and other small projects work well with fat quarters, where a quarter yard would be too long and narrow.
I also buy them as souvenirs when I'm travelling. When it's just a fat quarter, I don't feel like I have to use it; I can save it for as long as I want. Many of them do make their way into quilts eventually, but I don't feel any obligation to use them.