I'm starting to get tired of Ramsay myself. I kind of hope he gets killed soon. There really is not much emotional impact left when he kills someone or generally does something 'evil'.
Sorry to bring it back to the power of books over TV, but I think it's interesting. I'm finding a lot of the plots / characters on the shows starting to get dull, or stagnate. I think it's because a TV show has to give these things regular screentime. Ramsay is the best example. In the books, he doesn't actually get that much 'screentime'.... But through Theon's thoughts and recollections, plus various accounts of his actions going back (I think) to the first book, the reader knows all about him. In the show, to get the viewer to understand what he is all about, they need to constantly show him doing 'evil things', which starts to get stale after a while.
Also worth pointing out that he has been a regular in the show since Season 3, where he basically spent the whole time torturing Theon. And Theon has been a regular since the very beginning. In the books, after the sack of Winterfell, Theon is not seen or heard of for several books. Everyone thinks he is dead. When he pops up in the 5th book, it's a really shocking moment. "Holy shit, that crippled old man is THEON! What the hell happened to him?" And all the torture and abuse he has been to is detailed (or at least hinted at) though his thoughts and recollections, which is how the reader really gets to know Ramsay. In fact, there are I believe only 6 (I think?) Theon chapters in that one book, but they cover a hell of a lot of ground.
What else we know about Ramsay precedes the sack of Winterfell. He has a bit of a reputation before then. When Robb is off fighting and Bran is left in charge of Wintefell (so before Theon takes Winterfell), one of the domestic issues Bran encounters it 'The Bastard Of Bolton', so we know of him by reputation waaaaay before he actually appears. Lots of northern lords are wanting to marry the recently widowed Lady Hornwood with hopes to inherit her estate. Ramsay marries her forcibly, 'disposes' of her and claims all her lands for himself.
Anyway my point is, in the books Ramsay has been there since the beginning and is still a very interesting character. In the show, I am just bored of seeing him killing people.