Running 10.9.2, I have gone in to SysPrefs and made sure Keyboard>Text is set to NOT auto-correct, I have gone to Mail Prefs and made sure spell checking is done after I finish, but no matter what I try, I can type a valid word (I do have to use some science words, and of course company and personal names) and auto-correct changes them to some crazy "corrected" word in a flash! I have to delete and try again, sometimes it works, more often it gets replaced again! This is annoying.
I saw another question with an answer that told of an overlay showing the original word and how to use arrow keys and enter to replace what was correctly written in the first place; that did not work in my test on an email messsage. Just as a test here (Safari browser), I wrote "c o o l g o n i a n" but without spaces) and it is turned into "Colonna", capped and everything!
What might I be missing? I wondered if there is a plist file I might remove to re-do a prefs for the Mac?
CLARIFYING: While I appreciate the info on turning off spell-check in browsers, I guess I failed to state that this is a system-wide problem, not just in email or browsers. If I write that cool word in Adobe Illustrator, it also changes it to Colonna. So I guess I'm stuck with it, but it makes me nuts trying to enter words "correctly" that get corrected as soon as I hit the space bar!