I put source code/IDE/logging output in one, and the program I'm running in the other, particularly when debugging a program; running in debug mode or watching logs is simpler.

I also put remote desktops in a separate screen, often copying the contents of configuration files over as text, as I don't generally get the ability to drag files directly into environments (people who prevent direct copying of files or dragging and dropping, your security is getting in the way without providing any security - Base64 encoding exists).

Otherwise I will have social applications open in one (e-mail application, chats with clients, etc), and my actual work in the other.