I've got a simple (for me) use case for which Google completely fails every time. It's mostly for programmers/sysadmins though. Paste an error message from a daemon, kernel etc in google and see what you get. With a little luck, 95% of the results on the first page won't be related to your problem. I'd say 20% won't be related to the piece of software you're dealing with at all.
This can be sort of mitigated by selecting 'Verbatim', but for some reason you can't turn that on forever, you have to select it on every search.
Add censoring of search results, and Google loses its usefulness completely.