Castle and Beckett's First Kiss — Without Background Music! (VIDEO) Tweet January 25, 2013 at 11:12AM EST by Wetpaint Entertainment Staff Related: Castle, Caskett , Richard Castle , Kate Beckett , Season 3 , Season 5 Episode 13 Credit: YouTube Remember Castle and Beckett's first make-out session back in Castle Season 3? As if you could forget! Now you can relive the moment in its most real and honest state — without background music. Enjoy!