I'm developing on multiple computers. If I deploy to my phone directly from Eclipse on one computer, I can't deploy from the other without uninstalling first. I'm assuming this is because there is a debug certificate being used to sign the app, and they're not the same across the two machines.
Is it possible to copy one over to the other so that Eclipse is using the same one on both machines?
Yes.
In Unix like os the debug key is located by default in ~/.android/debug.keystore
You also can choose a custom one from eclipse like in the following screenshot: