Online surveys are generally considered cheaper, faster, and more convenient. They also have a potential for international reach, allow for elaborate skip-logic, and eliminate errors in data-entry, to name a few of their benefits.
But many wonder about their validity.
In this paper all the important threats to the validity of both online and offline surveys are assessed. Such as lack of a sampling frame, and things such as experimenter effects.
As long as the pros and cons are taken into account, there is room for both, and with the arrival of smartphones, there might be a sampling frame for web-surveys soon.