My dad does not like gifts. Every Father's Day I tell him I got him the same thing: the knowledge of knowing that I didn't spend any money on something he doesn't need. His response: "It's what I've always wanted."
He claims that we don't need a manufactured holiday to show how much we love our family. The same goes for Mother's Day, or someone's own birthday: You should feel special and appreciated every day.
This rule also works great to avoid crowded brunches on the first Sunday in September. Why not take dad out to brunch whenever you feel like it? (Yes, all of these apply to mum, too.)
Plus, have you seen store-bought Father's Day cards? They assume all paternal figures love fishing, golf, or woodworking. This holiday was not intended for the man who raised me. He likes falling asleep in the backyard while reading road atlases, so I'd need to make my own card (thanks, Papyrus). Imagine the delight of giving someone a handwritten card on a random day. Parents would love that. You would quickly become the favourite child, and your older sister won't stand a chance.