I did a local install of WordPress on Ubuntu 14.04 following the steps outlined here and simply running:
sudo chown -R www-data:www-data {path_to_your_project_directory}
solved my issue with downloading plugins. The only reason I'm leaving this post here is because when I googled my issue, this was one of the first results and it led me to the solution to my problem.
Hope this one helps to anyone!