* Regret for a past action or decision: "Je regrette de ne pas avoir écouté tes conseils." (I regret not having listened to your advice.)
* Sympathy for someone's misfortune: "Je regrette votre perte." (I am sorry for your loss.)
* Disappointment about something: "Je regrette de ne pas pouvoir venir à la fête." (I am sorry I can't come to the party.)
The context will usually make it clear which meaning is intended.