Try resetting home folder permissions and ACLs. If you have a permissions problem in your account, then it could be inherited to subdirectories in the account and propagate the problem. To reset this, reboot the system with the Command-R keys held down immediately after you hear the boot chimes. This will load to the OS X Recovery tools, and when you do so, select the Terminal from the Utilities menu.
In the Terminal, run the command "resetpassword" (all one word, lowercase), and in the utility that pops up, choose your hard drive, then your user account from the drop-down menu, and then click the button to reset home folder permissions and ACLs.
This should ensure all folders in your system are properly accessible, so when you drag items around they are moved by default, instead of copied or otherwise handled.
Alternatively, as CT mentioned, if you are using Command-C to copy a selection and then are trying to paste it in a new location with Command-V, then this will result in copying the files and not moving them.