I want to watch the TV show Hannibal (2013).
Do I need to watch the movies before I watch it, or are they independent?
The TV show depicts the events before the movie trilogy, in particular before Red Dragon (or Michael Mann's 1986 take on it, Manhunter, for that matter), showing Will Graham's work as FBI profiler under assistance (and care, given that the TV show depicts a significantly more deranged version of Will Graham) of Dr. Hannibal Lecter and thus the events before Hannibal's true nature is revealed and before his arrest.
Though, having seen not much more than the first few episodes of the TV show, I don't know if the later episodes might even venture as far as into the story of Red Dragon (or any of the later set/previous movies with Clarice Starling), but even then you don't have to watch the movies beforehand, it might even benefit the suspense if you don't.
The TV show is thus more or less a prequel to the movies (ignoring the rather infamous Hannibal Rising, which isn't necessary for the story either, though, being in turn set before the TV show). So while it may add to the enjoyment of the TV show to be acquainted with the characters (and see/compare the different takes on them), it is absolutely not required to understand the characters or the plot in any way. So no, you don't need to watch the movies, they are more or less independent (or rather later in the chronology).