Two words: Halo headband
I got turned on to Halo brand head bands three or four years ago when I moved back to the muggy Southeast. These things are just plain awesome in every way. They incorporate a rubber band across your brow to "dam" and channel the sweat away from your eyes. The super absorbent material soaks up the sweat and transports it to the outside of the band where it sort of evaporates depending on how much you sweat.
They are quite thin and I barely notice I'm wearing it. If I'm on a long ride and sweating a ton, once it gets sweat-logged the extra sweat just drips down my sideburns and not my eyes. If I think about it, once in a while I stop, wring it out and keep on truckin'.
I have three of them including a "bandana" head cover that covers the top of my "streamlined" head from the sun. These things really save your helmet liner too.
Recommend them highly: