The starburst clock, like the deer head(link), shows up in numerous episodes each season. It is a visually interesting but non-distracting item for set decoration. The clock first appeared in Bloody Mary (cite link). The clock is not limited to hotel rooms. It has also been spotted in diners, businesses, and homes.
In Yellow Fever (link) Dean destroys a similar looking clock but it is not the true star burst clock. (need pic)
(Need pic of clock from bloody mary, diner in 302, etc)