Another idea not mentioned yet is to request that gifts be given to a charity in lieu. For example, setting up a Just Giving page.

The OP mentioned that this might seem crass; One way to make this less crass is to make it clear that not donating at all is perfectly fine.

> You don't have to get me anything at all for my birthday this year but if you'd like to give something, charity donations to my preferred charity <insert charity here> would be a welcome gift.