Magento Connect: “Warning: Your Magento folder does not have sufficient write permissions.”

The following is 100% safe to run from the directory where Magento is installed:

find . -type f -exec chmod 644 {} \;
find . -type d -exec chmod 755 {} \;
chmod o+w var var/.htaccess app/etc
chmod 550 mage
chmod -R o+w media
If that is not working, try setting all directories to 777 by doing this:

find . -type f -exec chmod 644 {} \;
find . -type d -exec chmod 777 {} \;
chmod o+w var/.htaccess
chmod 550 mage