How to Suppress Repetition of Warnings That an Application Was Downloaded From the Internet on Mac OS X?

To remove the quarantine alert you can run the following command in Terminal:

xattr -d com.apple.quarantine /PATH/TO/APPLICATION

You may need to run this is an administrator depending on the permissions on the resulting application (as you said you don't run as administrator). If the application has permissions set that you can't remove the metadata with your user account it explains why it comes up every time. You can either run it as an administrator on your computer or run the command above as an administrator. (Use su admin_name if necessary)

To stop this from happening in the future, go to Terminal and type this (hitting Return afterwards):

defaults write com.apple.LaunchServices LSQuarantine -bool NO

Source: MacWorld

Or — simpler yet — download Secrets and search for “quarantine.”