utf 8 - UTF-8 html without BOM displays strange characters

I have some HTML which contains some forign characters (€, ó, á). The HTML document is saved as UTF-8 without BOM. When I view the page in the browser the forign characters seem to get replaced with stranger character combinations (€, ó, Ã). It's only when I save my HTML document as UTF-8 with BOM that the characters then display properly.

I'd really rather not have to include a BOM in my files, but has anybody got any idea why it might do this? and a way to fix it? (other than including a BOM)