Finding data created by a certain application? I'm looking for the data-store of a certain application so I can take backups of some files that are important to me. Connecting the phone to my computer and browsing the file-system I get revealed a surprisingly empty file-system.

Is the a generic way of locating data created by a certain application on the phone? Since Android tracks the storage use on a per-application basis, I assume there is a register somewhere, but I don't know where to look.
Android can't/doesn't keep track of arbitrary data created on the SD card.  If you're looking for regular app data such as settings, it's located at /data/data/qualified-app-name where the name is something like com.rovio.angrybirds for Angry Birds, for example.

As eldarerathis notes you'll need to be root to view the data partition; it's protected to prevent malicious apps from stealing your data (etc.).