What is the purpose of the little eyebrow windows on the Boeing 737?
From Wikipedia: Boeing 737:


  Most 737 cockpits are equipped with "eyebrow windows" positioned above the main glareshield. Eyebrow windows were a feature of the original 707 and 727. They allowed for greater visibility in turns, and offered better sky views if navigating by stars. With modern avionics, they became redundant, and many pilots actually placed newspapers or other objects in them to block out sun glare. They were eliminated from the 737 cockpit design in 2004, although they are still installed at customer request. These windows are sometimes removed and plugged, usually during maintenance overhauls, and can be distinguished by the metal plug which differs from the smooth metal in later aircraft that were not originally fitted with the windows.


Boeing has also determined that removing the windows reduced the cockpit noise by about 3 decibels. The newer models have 10 vortex generators above the cockpit where the windows used to be. It also reduces maintenance costs.