To me thy are almost more important then gameplay at times.
I get really immersed into a game. I applaud the MGS series and Mass Effect for having the best damn fiction I have seen. Kudos to them. If a game can really make me cry (MGS) or feel like a hero (Mass Effect) then I will gladly pay money to it.
P.S: GTA4 has a pretty good story even though it is more satire on criminals and social norms, doesn't touch my heart but my head.