The first time they kiss on screen is in season 3's 'The Santa in the Slush' when Caroline demands they kiss under the mistletoe in exchange for her pulling strings to get Brennan the use of the prison property trailer to spend Christmas with her father.
Technically, however, the actual first time they kissed was during their first case together which was flashbacked in the 100th episode; season 5 episode 16: 'The Parts of the Sum of the Whole'.
Well it depends. On screen they kissed in Season 3 The Santa in the Slush. But in Season 5 The Parts in the Sum of a Whole its revealed that they kissed on their first case together. Hope that helps.
