The rule of thumb about italics vs. quotes is "big things get italics, little things (or pieces of big things) get quotes."
If it's the name of a book or magazine, italicize it.
If it's the name of an article or blog post, put it in quotes.
If it's the name of a movie, italicize it.
TV shows have become debatable, because they are getting "bigger" in the sense of being longer and becoming more important. So I think you'd have to consider the context.
- If you talk about TV shows and movies in the same piece, use quotes
for the TV show. (Basil Rathbone in The Hound of the Baskervilles vs. Benedict Cumberbatch in the BBC's "Sherlock")
- If you are only talking about various TV shows, use italics. (Benedict Cumberbatch in the BBC's Sherlock vs. Jonny Lee Miller in CBS's Elementary)
- If you are talking about a TV show as a whole and the names of
various episodes, use italics for the show name and quotes for the
episode names. (Sherlock's Season 3 was "The Empty Hearse," "The Sign of Three," and "His Last Vow")
If it looks silly that you're italicizing the name so many times, maybe you need to edit the piece so you aren't saying the name so much.
ETA at Neil's request While this may seem contrary, I would say that a series of books which has a formal title doesn't get formatting at all: the Lord of the Rings trilogy, the Last Herald-Mage trilogy, the Belgariad, the Malloreon, the Dragonriders of Pern series. My instinct is that each of these is a name for a collection of things, an umbrella term, rather than a proper name.