On latest Ubuntu distributions (based 16.01 LTS) Kodi's add-ons won't connect to the internet due to a bug in the systems python-openssl package, wihich is outdated. They throw following error to the logs:

URLError: <urlopen error [Errno 0] Error>

So uninstalling the system package and upgrading to pyopenssl using pip worked just fine.

# sudo apt-get remove python-openssl
# sudo apt-get install python-setuptools python-pip python-dev libssl-dev
# sudo pip install --upgrade pyopenssl

Add-ons are working afterwards.