The disadvantages of free online sheet music have already been pointed out, so a couple things in favor of them:
Firstly, and to me, most importantly, sheet music books (rather than individual scores) are a pain in the butt to use. Pages are constantly turning when you don't want them to, I find myself folding the book so that the pages stay put! By the time I'm done with one or two pieces, the book is not what I'd call in good condition.
Online sheet music, on the other hand, can be printed and nicely placed into a binder that basically gets rid of the above problem... furthermore, even if something happens to the version in the binder, you have it backed up on your computer ready to re-print on a whim.
On a related note, keeping your scores organized is obviously quite easy on the computer -- you also don't have to worry about losing it.
And of course, often times it's free!
And BTW, I still go out and buy sheet music, obviously, because you can't find everything for free online, and, as others have said, it is always best to compare editions and scholarly notes. But there is certainly merit to the online method, as well, IMO.