I always wear either skull cap or helmet liner(similar to skull cap but no tie ends) under my helmet. There are a few reason to use these.

* Keep your sweat from running down the face.
* It keeps your head cool. The sweat takes the body heat with it when it evapolates.
* It keeps the inside of your helmet cleaner.

I have tried many differnt types, and here's a several of the things I learned.

* No cotton. Synthetic such as polyester are the best. They don't hold the sweat but wicks it and spreads it in wide area, which helps the sweat evapolates quicker. (I have not had my skull cap or liner soaked all the way. It usually starts from the rim of the cap then toward top of my head but the top of my head had never been completely wet. And my helmet has a lot fewer vents than most bike helmets do. It's a BMX helmet.)
* No multiple purpose garments. Liner that made to fit just for the head is better. Under the helmet, not enough room for extra material. Avoid bandanas.
* Stretching material make more contact with the head, therefore wicks more sweat. The same way Underarmor works.
* Mesh material helps the sweat evapolates quicker.
* Thinner, tighter the materail, wicks the sweat quicker.
* Make sure that material covers big part of the forehead where the sweat production is at the most. Pull it down low.

The best place to see what kind of helmet liner works best is to watch football player on the side line. If it works for them, it works for cyclist, only better. Because the cyclists move more air than football players do.