Personally we always do no gifts and my kids have learned that a party is spending time with friends and family and celebrating! They get gifts from us on their actual birthday and get to pick a special dinner as well. It's never been an issue for them
At first people still showed up with small gifts, but quickly realized we really do mean it! Our kids have plenty of toys and we always end up donating a lot of what people buy them. I doubt the family would have put it in the invite if they didnt mean it!!