So basically how could you tell if anyone copied any file from your computer ?
If the file was stored in an OS with a secured filesystem that had the ability to log the timestamp of all reads/writes to log file and the UserID of the person accessing the file(s) it would be easy.
Under Linux 2.6 kernel (and later) this can be achieved by enabling the Linux Audit Daemon
If you are using windows, there is a basic check, depending on the exact OS your using the procedure may differ slightly:
Right-click the folder that the file is in, click views>details.
Right-click the folder again, click "sort by" and check the "date accessed" box to see when the file was last accessed.
If it's more recent than the last time you accessed the file, it would imply that someone else has handled the file.
Maybe there is a better way under MS Windows, but I don't use it enough to know.
EDIT: I did a bit of Googling, maybe this will help http://support.microsoft.com/kb/310399
In Windows 7 it could be setup by using the "Local Group Policy Editor" by enabling "Computer Configuration\Windows Settings\Security Settings\Local Policies\Audit Policy\Audit Object Access". Once enabled then each file should have a new Properties\Security\Advanced option to log read/write/modify access when you right click on any filename.