When you either first set up your Mac, or if you have upgraded it to the latest versions of OS X, you will find Apple has changed some of the default spell checking services to auto-correct typographical errors.
While in many cases autocorrect can be convenient, there are times when it can be a burden, especially if you are intending to use misspelled or non-standard words.
In these cases, you might find yourself pressing Command-Z all the time to undo the system’s changes, but instead of resorting to this, you can turn off OS X’s auto-correct services, and instead only have it indicate a potential misspelled word.

With auto-correct disabled, misspelled words will be underlined in red. You can then right-click them to choose from a list of suggestions.
This setting can be done on a per-application basis. To do this, you will need to find the “Spelling and Grammar” settings in the program, which in most cases are a submenu in the Edit menu. In this menu, you should see options for correcting spelling while you type, and automatically correcting spelling and grammar errors. A check will appear next to the options in this menu that are enabled, so just select the desired menu options to toggle this check.

Uncheck this option to disable autocorrect system-wide (click for larger view).
System-wide
The spell-checking service in OS X can be adjusted system-wide. Just go to the Keyboard system preferences, and then click the “Text” tab. In here, you will see the settings for text substitutions, next to which you will see a checkbox for “Correct spelling automatically.” Unchecking this will disable auto-correct system-wide.
Regardless of how you approach disabling autocorrect, when done, instead of the system changing your typed words, it will underline them in red to indicate a potential problem. You can then right-click the word to get a list of suggestions from Apple’s built-in dictionary, but can also choose options to learn or ignore the word.
Great!
This appears only to work for Mavericks. Can it be disabled on Mountain Lion?
It should be available in most recent versions of OS X. The settings for it in the system preferences may be in the “Language & Text” system preferences. I can’t be certain right at the moment.
I’m using OS X 10.7.5 Lion and auto-correct is, as you suggest, in Language & Text under Text. It’s probably the same in OS X 10.8.x Mountain Lion. Apple did some serious regiggering of the system preferences in OS X 10.9 Mavericks, which will make tutorials like this somewhat problematic going forward unless you have multiple systems available for testing. One solution would be to use VMWare Fusion or Parallels Desktop to run an older version of OS X, but I don’t know if that’s possible yet.
I’ve found that Apple’s built-in dictionary is pretty anaemic when it comes to spelling suggestions – for instance it had nothing to offer when I misspelled anaemic. I use Spell Catcher X (https://www.macupdate.com/app/mac/10590/spell-catcher-x) which has many more and more complete dictionaries (for languages other than English and for profession specific technical terms – you can download and install only the ones you need), including a shorthand/shortcut glossary for frequently used words and phrases, and a similarly functioning auto-correct glossary for words most often misspelled – to which you can add items for your own spelling tendencies – like spelling misspell with only one s or l.
You can create any number of user dictionaries, say for specific writing projects, which I do so that my user dictionaries don’t become too cluttered to search easily.
At $39.95 Spell Catcher X may be too pricy if you don’t do much writing, but for long-winded bloviators like me (a word Apple’s dictionary doesn’t know) and serious writers it is worth every penny – that is if you care about correct spelling, are prone to typos, and are not a spelling bee champion. Being a mediocre speller myself, I’ve used Spell Catcher since my early days on a Mac back in the mid-90s.
I just found out that the author of Spell Catcher X, Evan Gross, passed away recently so the future of Spell Catcher is up in the air. It has not been updated for Mountain Lion and Mavericks and may behave erratically there.
Oh, what a blessed relief, thank you so much! I write a lot of mails containing (British) English, French and German simultaneously and the autocorrections were driving me mad.
Since you write in several languages, in your case it may be best to set up the spelling tools differently from the default. Go to the Keyboard system preferences and click the “Text” tab. That’s the one pictured next to the “System-wide” title in the article.
You will find a drop-down menu under the word “Spelling:” on the right side of the panel. You probably have it as “U.S. English”. Change it to “Automatic by Language”.
Now choose “Set Up…” in the same drop-down menu. Activate “British English” and drag it over “U.S. English”. You may alternatively simply uncheck “U.S. English” if you don’t really use it.
You may also want to drag “Français” and “Deutsch” closer to the top, and maybe uncheck languages you never use.
Strod: The instruction you offer are for OS X 10.9 Mavericks. For anyone using an earlier version of OS X, the solution is different. It’s in the Language & Text system preference. You will find the option to use more then one language at a time under the Language tab; to add or remove languages click the Edit button; you can change the sort order to that for a specific language with the Order for sorted list pull-down menu. Text options are under the Text tab where you can set the spelling Automatic by Language as well as turn off Correct spelling automatically. Date and currency formats are under the Formats tab. And you can select which languages to activate under the Input Source tab; if you check Show Input menu in menu bar you will be able to easily change from one language to another when you need to.
The Mavericks preferences may be better organized (though that’s a matter of opinion), but not everyone is there yet.
Does anyone know how to NOT automatically choose the language used for spell check but QUICKLY switch between different languages (like switching between input sources). I know you can go to system preferences and hard-change the spell check language, but that takes a long time when you switch often, and automatic has the problem that it will accept some words it mistakenly thinks are English, but they are not correct when writing French.
Spell Checking does not work at all in Yosemite, either from system pref. or from Word pref. Settings are correct but no go for spelling.