Can I get auto-completion for words in Microsoft Word 2010?

There is Phrase Express (freeware).

Organize frequently used text snippets.
Expand abbreviations as you type.
Launch programs with text shortcuts.
Auto-complete repetitive phrases.
Quick access to the Windows Clipboard History.
Correct spelling mistakes in any application.

You can also create your own suggestions to auto-complete...Works on Windows, cross-software...

Also: Alternatives to Phrase Express.

There is not AutoComplete in built into Word such as you'll find in a web browser or the like simply because the possible words you'll type into a Word Processor is much, much larger than the list of possible words you'll enter into a browser address bar.

Microsoft did re-enable a system called QuickParts or QuickText that allow you to enter a pre-defined code or set of keys which Word will then replace with a longer phrase that you had configured previously.

You can find more information on this built-in system here and here.