Ren's watch is a watch of Ren Tsuruga. He uses this watch in order to keep control of himself and in order to remember how Rick died and the reason he thinks how he died. The watch played quite an important role in the Dark Breath arc.
After Ren (who is acting as the fairy prince, Corn) got the "kiss of re-birth" and stole a kiss from Kyoko, he decides to switch where the watch is placed on his arm. He switched it on his right side instead of his left side, indicating that he changed a little bit and forgives himself, but is still not convinced that Rick or Tina has forgiven him or will ever forgive him.