intellij idea run configurations backup

Its here .idea\runConfigurations (correct for Idea 11). Just copy this folder to new project.

EDIT: As per comment, if runConfigurations folder doesn't exist, check the 'Share' box inside the Run/Debug configuration

The location would depend on 2 factors, whether the configuration is local to the user or shared with the other developers and if you are using the file based (legacy) or the directory based project format.

• File based project, local configuration: .iws file
• Directory based project, local configuration: workspace.xml file under .idea directory
• File based project, shared configuration: .ipr file
• Directory based project, shared configuration: .xml file under runConfigurations subdirectory of .idea directory or files inside .run directory in the project root (you can customize the location of the shared configurations in the latest versions).