I had the same problem, and discovered it is related to the Send to Bluetooth add-in
Launch Visio, go to Tools -> Trust Center. Then select the Add-Ins option on the left. At the bottom of the screen, press the Go button to Manage COM-Add Ins. You should disable and remove the 'Send to Bluetooth' option.
Visio was crashing anytime I did anything: copy, edit text, open a file browser. I am running Windows 7 64 bit with Visio 2007. So far, this has resolved the crashes for me.