This is an excellent question. I think it can actually matter a lot, at least in some cases. (Disclosure: I am on the faculty of a research university, and of

This is an excellent question. I think it can actually matter a lot, at least in some cases. (Disclosure: I am on the faculty of a research university, and of course I don't want to think I'm wasting my time or my students' time. :-) There are a couple reasons. One, as mentioned by other posters, is that the advisor can have a lot of influence on choosing good problems to work on; in my field (applied mathematics), it can be tempting for a bright student to focus excessively on interesting but narrow technical problems, or on chasing flashy things that have little depth or substance. Second, precisely because of how much material is published these days, beginners need a guide to the field. For whatever it's worth, a good advisor's job (I think) is to put new findings in context, which is increasingly hard to do on one's own. In short, one significant way in which the advisor can have tremendous influence has more to do with decision-making, and not so much fact-finding (although sometimes that is important too).