I worked with a client recently and one of the last tasks in our work together was cleaning off the desk. We did so much work sorting through all the paper - purging, shredding, organizing, and filing. Once we found a home for her important documents, we tackled the desk which had turned into a catch-all (I have the same issue in my entry way but more on that later).
We sorted through the final stack of papers and bills on the desk, set up a To Do / Action Items filing bin that, once it got full, needed to be reviewed (pay a bill, scan a document and shred the original, etc).
I like that this desk has a lot of character and now it can be more useful than just the catch-all station for storing things. My client can still easily access the items that make sense to keep on the desktop, but now has a clean surface to work on as well.