Five, with any degree of proficiency. Native Greek, near-native English, licenced to teach French, close to licence level Spanish, decent Italian.
If dabbling counts, the list grows exponentially to include Latin (pretty drilled into me at school, but I'm way out of practice), Japanese, Russian (one and two years of classes respectively, but a long time ago), Portuguese (half a year of online study) and Scots Gaelic (some self-study).
Languages are my obsession. I don't know if the list will have more items added (I do want to learn Turkish one day, though, as well as make use of my Philo-Celtic Society membership), but I definitely want to pick up some of the less-studied ones again.