From 1.01 Pilot until 5.07 The Curious Case of Dean Winchester, Dean always wore a bracelet on his right wrist, with few exceptions. In season 1, he wore an elephant hair – style bracelet. Based on mythology, this brought good luck and protection from harm and illness. The bracelet is missing in season 2 (2.01 In My Time of Dying, 2.02 Everybody Loves a Clown, 2.03 Bloodlust), and it's likely it was lost or broken in the car crash at the end of season 1.
Season 2 onwards
From 2.04 Children Shouldn't Play with Dead Things to 5.07 The Curious Case of Dean Winchester, Dean's elephant hair bracelet is replaced with a skull prayer bead bracelet. This type of bracelet originated in Tibet and is said to assist with contemplating the meaning of life and death during meditation. From 5.08 Changing Channels, all of Dean's jewelry has been removed; his signature silver ring and the skull prayer bead bracelet are gone and only his watch remains.
See the explanation from Jensen Ackles and the removal of jewelry from season 5 onward.