I also feel that a personalized* "thank you" is necessary for politeness, but specifically being a written "note" is not--verbal in-person, over the phone, email, handwritten note in the mail, etc. are, in my opinion, all polite options for thanking a giver.
*By personalized, I mean making some amount of effort to acknowledge the specific person and the gift they gave. This is in opposition to one blanket "thanks, everyone" statement at the end of an event, for example.
I also think that a written thank-you (whether email or a piece of paper) ought to be somewhat personalized, and not just a generic "thank you." For my cousin's child's birthday party, we used to get a nice photo card in the mail with pictures of the party on it and an ornate "Thank you, love the Smiths" text printed on it. But, the pictures were not pictures of us at the party, or of the gift we gave; and there was nothing typed or written on the invitation to make it personal to us. In other words they printed out a dozen of these things identical and sent them to all the guests. Points for sending something, I guess, but I didn't get why they couldn't add "thanks for the books!" or our names or something like that. I would be totally cool with having the whole thing typed if writing by hand was tough for them, or just having personalized pictures if words weren't their thing, but a generic thank you card is, to me, little better than the mass "thanks, everyone!" at the end of the party.
BUT, I do think that gets into a grey area, which some people would say was too picky or demanding, and I wouldn't want to discourage someone from sending TY notes because suddenly they're afraid there's a complex, subtle formula they have to follow, rather than just saying "thank you."