I look out for teams from places I've been to and liked. So I like to check the scores of Lille, Rennes, Bayern/1860 Munchen and a few other teams dotted around Europe. I'd say I follow their scores though, rather than properly supporting them.
I loved Valencia ever since they played Celtic in the UEFA Cup in 2002, but I also have a soft spot for Partick Thsitle and Queen's Park, being Glasgow teams. But I've noticed I like teams for having an underdog tag, or for a former player playing for them or something (Paul Lambert managing Norwich, Lambert playing for Dortmund, etc)