There are many advantages.
1). You can increase the sample size by distributing them to a lot of people.
2). If they are anonymous, people may feel more comfortable than administering them in-person.
3). They may increase external validity because their responses may generalize to a larger audience.
4). Depending on their validity and reliability, they can accurately measure behavior.
Disadvantages:
1). Lack internal validity. You cannot establish causality with surveys.
2). If conducted in face, people may not be comfortable answering questions that are highly sensitive (e.g., sexuality).
3). They are limited, in that manipulations cannot be done.