The right hand is the traditional hand for vows or oaths. A traditional reason to wear the wedding ring on the right hand stems from Roman custom and biblical references. The Latin word for left is "sinister", which in addition to this sense also has the same senses as the English word. The Latin word for right is "dexter", a word that evolved into "dexterity". Hence, the left hand had a negative connotation and the right a good one. For the same reason, an oath is sworn while raising the right hand.
The left hand is also used for cultures that believe in the vena amoris or "vein of love" that is believed to be found in the left ring finger.
However, the most widely accepted explanation is that because the majority of people are right-handed, wearing the ring on the left hand makes it less likely to be damaged or lost during everyday activities.