Just like all librarians, I'm on the fence about Google and other search engines. Very useful - irreplaceable in some situations - but not always used appropriately and certainly not understood well enough to properly judge appropriate use.
I just came across another specific disadvantage of the "just google it" phenomenon. People in institutions with large websites seems to think that it's ok not to organize their site well since you can just site-Google what you want anyway. Even those who are invested in a specific area of an institution think it's just fine to have the primary (pronounced "easiest") access to their pages be through the Google search engine limited to the site's pages.
By itself, this is not necessarily a bad thing. It DOES provide quick and easy access to what users want without having to find their way through a long and complicated site structure, particularly for complex issues that aren't important enough to warrant front page real estate.
The problem is that it relieves us of the job of having to think about our desired information goal on a broader level. But is this a problem? Thinking is hard. It takes effort. And when we want information yesterday, we don't want to waste time thinking about something only tangentially related to our want/need. Having to think about, say, what KIND of thing is the thing we want to find, or WHY would the institution be providing this information and therefore where would they have made it available, is complicated and requires effort. But I think it's important in almost all situations.
Actually, I think there are only two situations: either it's easy to do this since the answer is obvious, or it's not so obvious and therefore is going to take some time and energy to figure out. The first case is not a problem. Finding information about "Dogs" should be in a book about "Animals" or in the "D" section or in the area related to "Pets". No problem. Find that section/chapter/link/section and go there. Problem solved. However, what about something like "Student Initiatives"? What is that exactly? The searcher themselves may not understand what exactly they are looking for. In fact, that may be WHY they're looking for information in the first place, because they don't know what that phrase really means. And without that information how will they be able to find what they are looking for if (a) the site is not using that phrase exactly, or (b) the phrase is being used in two or more different ways? Spending some time before searching to think about what the topic being searched for actually means, or even just COULD mean, would ensure that the searcher will be able to find the information faster and, when finding it, more quickly identify it as the information being searched for. Mere "phrase recognition" can lead to dead ends or mistakes.
Of course, all this relies on the pile o' information being searched is well organized in the first place, which, I guess, is the intitial stumbling block. This too is hard work and requires a lot of time and effort. This is certainly why it doesn't always get done in anything but those "piles" for which information searching is the primary purpose of the pile (e.g. journal article indexes). Web sites are not usually primarily about find each piece of information they contain. They are usually marketing tools to some degree. Communication of pieces of information chosen by the owners is the focus. But if the owners of this information want it all to be found, not just the pieces they want, then IMHO then need to ensure more finding tools that Google Site Search.
My 2.0 cents.