Yes, people should acknowledge a gift. I read through all the responses, and everyone agrees.
The problem is that their NOT thanking you for it is causing you unhappiness and stress... and if that's the case, you shouldn't give them a gift at all. Gifts should only be given because YOU want to give them, not with any expectation in mind. They are, after all, gifts.
I admit that I am unsure what to do with gifts. I've read FIVE LOVE LANGUAGES, and I realize that gifts, of all acts of love, are completely unimportant to me. Much of this comes from my past, for my mother put all her "love" into stuff, and I realized over the years how little it meant. I am far more likely to watch someone's kids so they can have a date night than actually give them anything. But if I do give them something, I like it to be anonymous, so that they have no obligation in return.
I know this is not a popular opinion, but writing thank you notes as a kid--especially for gifts that were neither thoughtful nor kind--was pretty traumatizing. To this day I will e-mail thank you messages--or call, or tell them thanks and give them a hug--but the idea of writing on a card makes me cringe.
Just my perspective. Do what you need to do to feel happy with what you do. Remember, there's no way to change all of them, so it means you might have to give up gift giving (I can't believe I just wrote that!) or change your level of expectation. Then the rare thanks you receive will make you joyful...