Is there an application that executes commands on a server computer?
The only application I can think of is Mobile Mouse; its purpose is to use an iPone/iPod/iPad as mouse to control a Mac.

One of its features allows to have some icons on the iPod/iPhone that invoke some applications on the Mac; by default, the icons shown on the iPod/iPhone are the ones that appear in the Dock, but you can select a directory containing the applications or the scripts you want to execute.





The last screenshot shows the list of icons shown when I select a directory containing other directories; when you hover over an icon, the application shows the icon name, in the same way the Finder does. The icons with an indicator light are running applications.

The server application is available from the App Store, while the application for iOS is available from the iTunes App Store.