C:\>WMIC product where 'name="Program To Remove"' call uninstall
...and you see "execution successful - returnvalue 1603" but nothing happened...
...you're not running with admin privileges. Do either:
Start->type "cmd", [ctrl]+[shift]+[return]
and in both cases say "yes" to the UAC query, if active. You can now rerun your WMIC command and it will work.