A great deal is lost in repudiating the analytic/synthetic division.
Philosophers of the early 20th century had high hopes that an account of analyticity could perform vital epistemological work. There were hopes, for instance, that such an account would explain how it is we are able to get our knowledge of mathematics apparently a priori (although Kant himself, with whom the distinction originated, believed mathematical truths were synthetic).
Even more importantly, many philosophers regard analytic truths as the principle and proper domain of philosophical investigation. This is the central claim of conceptual analysis and is supposed to explain the armchair nature of philosophical investigation.
The reason philosophers don't have to go out and do experiments to learn about the world is because they are not particularly interested in the world. Rather, philosophers investigate our concepts of things in the world. These conceptual/analytic truths can be investigated from the armchair in the usual way - i.e. by using thought experiments to elicit intuitions which are supposed to be deliverances of conceptual and linguistic competence.
Rejecting the idea that there are analytic truths undermines the traditional conception of the subject matter of philosophy AND challenges the principle methodological approach used by philosophers today.
Quines arguments were very influential in his time but are not considered nearly as convincing now, particularly in light of the now-famous response by Grice and Strawson (1956).
It is not entirely clear yet, what is to be gained from giving up on the distinction. The easy answer is that if the distinction is a false or unhelpful one then by repudiating it we get closer to the truth. We also get a different, and perhaps (as suggested by Williamson in his recent book "Philosophy of Philosophy") a more ambitious conception of philosophical investigation.
The Stanford Encyclopedia of Philosophy has an excellent article on the distinction which you can read here: http://plato.stanford.edu/entries/analytic-synthetic/