For me, it's things like using IMDB (:http://imdb.com") to look up the names of the actors in that movie I watched last night. I've always had a hard time with proper nouns, and being able to carry on an on-line conversation without a lot of "uh ... wossisname ... you know, the guy who starred in that movie, uh, whose title I forget, but it was about ..." makes me feel like a much smarter person.

Really, of course, it's not about intelligence at all (except perhaps the sort of intelligence it takes to come up with good search terms), but it is about storage and retrieval. The Internet gives me a vast, constantly growing storage bank, and tools such as Google give me a retrieval system that's sometimes more reliable and easier to use than my own brain.