I prefer synthetic stocks for the following reasons:
1) generally lighter,
2) strong and rugged without concern for scratching, etc.,
3) NOT AS SUBJECT TO WARPING!!!
I'm surprised that wood is currently leading the poll. I own (currently) 17 rifles and ALL of them are synthetic except one (which is a Tikka Deluxe - which I bought as my "Rolls Royce" rifle - you know, more show than go.)(Oh, I forgot that I also have a Tikka Laminated SS - so then I have 2 wood stocked rifles.)
For me, I want a gun that is like a true hardcore SUV - take it anywhere and don't worry about scratching it.
Granted, plastic stocks are really not "synthetic." For me, true synthetic stocks are McMillan, HS Precision, etc. The cheap plastic injected molded stocks on certain Factory Remchesters are junk. Still, I somewhat prefer them over wood because you just can't damage them. AND, although they feel like junk, my guns are still very accurate.
Zachary