Personally, I think Thank You notes are important. I went to a baby shower in December for DH's nephew's girlfriend... still haven't gotten a thank you note! (And I gave her a lot of stuff.)
I have my kids write thank you's for their birthday gifts and for Christmas too, and I do the same. (Regardless of whether the gift was given at a party or mailed to them.)
I know they probably aren't needed for birthday party stuff, but I want my kids to know that some people do feel it is important, so they do should it. I do feel that they are mandatory for shower gifts, mailed gifts, and wedding/graduation gifts. However, that is just my opinion.