If we go by the following definition of Strong AI (from Wikipedia)

Strong AI is artificial intelligence that matches or exceeds human intelligence — the intelligence of a machine that can successfully perform any intellectual task that a human being can

then there are lots of things that Google can't do that many human beings can. For example, when you do an image search, the results are sometimes laughable, and that's because Google doesn't understand image content and just reports results based on the tags on the image or based on surrounding text. Lots of human beings would have understood the search query well enough to not return the results Google returned in many cases. So, Strong AI it ain't

Not to mention speech to text on Google Voice (usually laughable results) and translation (works a bit better, but breaks down hilariously e.g. http://groups.google.com/group/shibboleth-users/browse_threa... ).

Anything with a bit of judgment call about the kind of site you want returned is really bad, imo. Say I asked someone to search for blackberry-pie recipes, but specified I only wanted recipes from individuals, e.g. stuff posted on personal/university/etc. websites, not on content farms, TV cooking shows' websites, aggregators, etc. A human could trawl through a few dozen pages of results and pull out some recipes, but afaik there's no search term on Google that will do that.

It's also bad at summarizing information. I can get a scattered set of results for lots of topics, but it can't synthesize those results into a nice executive-summary paragraph for me. Never mind even better summarization, like searching for a topic that has no Wikipedia article yet, and having Google's algorithms write the article for me to read!