Wearing a ring on your left ring finger (of either hand, depending on one's culture) is an obvious sign of marriage or engagement, but here's a list of meanings of other fingers, provided by various Internet sources (which are only as reliable as the Internet itself):
Index Finger: Leadership, Executive Ability, Self-Esteem, Ambition for Power, Money, Spiritual/Religious Authority. Any emphasis on the index finger will tend to express the qualities of leadership, executive ability, ambition, and self-confidence.
Middle Finger: Responsibility, the Law, Justice, Sense of Right and Wrong, Discernment.
Ring Finger: Love (Romantic), Creativity, Relationship with Others, Committment to a person or cause
Small "Pinky" Finger: Expression of self, Sentimentality, Social Status.
Thumb: Extravagance, frivolity, pretense.