Tristan Rhodes has compiled small but useful list. This is a good read for new Linux user. He suggests using open-source alternative app as first option instead of windows app.
When someone asks me if they can run "Windows Application X" on Linux, the first thing I tell them is to look for an open source alternative. For most Windows applications, there will be a high-quality open source alternative that can meet their needs. The biggest hurdle for non-Linux people is simply knowing that these alternative exist and how to find them.