In reply to luke1: wow i can fill a draw with all the hats ive bought over the years,i see it my quest to find THE hat!
The current favorite for biking/running(well jogging,actually more like shuffling really) is a Ron Hill beanie,its a thin stretchy thingy it keeps the wind out but doesnt allow you to get too hot,fits under a helmet nicely and they are cheap as chips!
Hope this is some help.
P.s. it is also very compact so takes little room up in the hat draw!