I don't wear a hat to keep the sun out of my eyes or off my head because I live in Michigan. I don't use it to line up putts because I don't put it on straight to start with. The only reason I wear a hat is because it looks cool and covers up the massive cowlick that has taken over the back of my head.
I always wear a hat when golfing. One reason is because of the sun. Another is just that I feel more comfortable playing in a hat than without one. Of course, looking cool on the golf course is always a big factor.
If you see a guy dressed in a collared shirt and khakis who holds his finish well, you might never know he's a complete hack. Plumb bombing, too, makes it look like you actually know what you're doing.
I don't know.. some people just aren't hat people. People tell me I don't look good in a hat, and that i should let me hair flow. The visor things don't suit my style I think, so i'll just let my hair out.