I just want the search engine to stop changing what I'm searching for. I don't want to have to quote every word like I have to do with Google to make sure that the word is actually in the page, and by "the word", I mean "the word I type, not a word that Google things may be similar to the one I typed". It's worst when you're searching for foreign words, product names, acronyms, or whatnot and Google tries to treat them as if they're English words and declines them or chooses synonyms.
"Did you mean X?" is fine. Even "Searching for X (see original results here)", if you're very confident that the person made a common spelling error or whatnot. But just going in and swapping out words as if this is expected behavior? Terrible. At least let me disable it if you want to do that...
Beyond all this: I do like how one can do simple commonn operations on Google - math, conversions, etc. The more of these the better IMHO, so long as they have a standardized format - be they tracking numbers, flight lookups, whatever. It's okay in my book to be a bit Wolfram-y.
Keep the interface plain, simple, the sort of thing that'll work on any browser, from a modern Chrome to a simple text-only browser. Only use javascript where it's not essential for the site to work. Here's an example of something that would be a good use of javascript: if you need to track clicks, like Google does, do it through javascript rather than by having a link redirect like Google does. I hate how I can't just right click and copy link on Google without getting some massive Google redirect link.
Just my thoughts. :)