As a romantic novels enthusiast, I've read countless books featuring all kinds of love stories, including those involving shy guys. Believe it or not, some of the more heart-warming relationships are those between the courageous girls and the timid lads.
In 'Eleanor & Park' by Rainbow Rowell, for instance, the shy guy eventually wins the girl's heart despite his shyness, largely thanks to his genuineness and sincerity. So, yes, girls do like shy guys, particularly when these guys are authentic, caring, patient and understanding.