I love wearing things on my head, so I'd definitely do something! If you don't like hats, there are some gorgeous fascinators out there. And if you don't like those, you could always put your hair up with a big silk flower or something. But there are so many cool styles of hats and fascinators, that there's really something to suit everyone!
I got married in June, and people (American and British) wore hats, fascinators or nothing on their heads. There's no firm rule - just do what you feel comfortable with!