Especially on search engines, sometimes I am searching for words in another language, mixed-language results, or even doing an intentional search for misspelt words. In my native Dutch his first example would already cause problems: "spelling" means the same as in English, but "speling" means margin/give (the noun) and I wouldn't want one to be auto-corrected to the other. The fuzzy search for names on Facebook makes the search pretty much worthless especially in case you have an unusual variant of a common name in your search - you can be sure the actual person you're looking for is listed after half a billion bogus results.
The whole trend of second-guessing the user and saying "you tried to do A, but we assume you meant B, so we're gonna do B instead" is one of my biggest pet peeves.