I don't have much interest in shipping in general, and I don't have a favorite, but there are a few ships I do like. In Star Trek, which is by far my most in-depth fandom, I like J/7, Kirk/Spock, Garashir, Kira-Dax, and a few others (not to mention, that show has some great canon relationships especially in recent series, like Mariner/Jennifer and Burnham/Book, and even sexier starships!)

Outside of Star Trek, the only one that comes to mind is Narumitsu (Ace Attorney). I'm sure if I went looking I could find a Doctor Who or Magic: the Gathering ship I like, but I haven't really been exposed to those sides of those fandoms.