If you want spellchecking for Latin, someone's made a pretty decent LibreOffice Latin spellcheck dictionary. And LibreOffice works on Linux, Window, and Mac, is open source, free, and awesome, so you should have it anyways.
After you install LibreOffice, follow these instructions to install the Latin spellcheck dictionary:
In LibreOffice, select Tools --> Extension Manager from the menu bar.
In the Extension Manager dialog click Add.
A file browser window opens. Navigate to the folder where you saved the LibreOffice
extension file(s) on your system. The extension's files have the file
Find and select the extension you want to install and
If this extension is already installed, you'll be prompted
to press OK to confirm whether to overwrite the current version by the
new one, or press Cancel to stop the installation.
After you are asked
whether to install the extension only for your user or for all users.
If you choose the Only for me option, the extension will be installed
only for your user. If you choose For all users, you need system
administrator rights. In this case the extension will be available for
all users. In general, choose Only for me, that doesn't require
administration rights on the operating system.
After this, in your document, go to Tools > Language > For Selection > More..., and in the Language box select Latin.
If you really want to use Word...
In Word 2003, you were able to go to Tools > Language and change the document language to Latin. It didn't do any spell checking, but hey, you got a little 'Latin' label in the bottom right instead of 'English' (or whatever language you use).
It appears they've stripped a bunch of the language options out of more recent versions of Word. To stop spellcheck, under Tools > Language you can always change it to a language that you don't have a spellcheck dictionary for (Latvian sounds close enough). Or you can check the box that says Do not check spelling or grammar.
Of course, if you want to be really geeky, you can always use Vim...