Blocked: wine start /unix problem opening .exe files with Wine

When I try to open an .exe file in Ubuntu 10.04 Lucid, I get the following error message:

The file '/home/user/Downloads/program_name.exe' is not marked as executable.  If this was downloaded or copied form an untrusted source, it may be dangerous to run.  For more details, read about the executable bit.

To solve the problem, right click on the .exe file, select Properties, select the Permissions tab and check "Allow executing file as program". Then hit the Close button.