Word was first released in 1983 and ran in MS-DOS. It helped pioneer WYSIWYG and an Apple version was soon added (in 1984).
The DOS version ran to v5.5, but with the rise of Windows was replaced by Word for Windows, v1.0 of which first appeared in 1989 (the DOS and Windows versions ran concurrently for a time).
There was a large version jump from 2.0 to 6.0 as a response to the strongest rival, WordPerfect
5.1 - the reasoning being that a 'version 6' would be more appeal
ing to consumers than a 'version 5.5', despite the fact that they were different
products (see version inflation
The next version was not officially called Word 7, but Word 95, to fit with Microsoft's OS branding at the time (e.g. Windows 95, Windows 98...). This trend continued with Word 97 (v8) and Word 2000 (v9). If you examine a Word file (for example, open it in a standard text editor), it does identify itself internally by version number (e.g. 'Microsoft Word 8.0'), but Word is publicised and sold under the 'friendlier' name (e.g. 'Word 97').
The current version (v10) is referred to by Microsoft as Word 2002, but the surrounding Microsoft Office suite is known as Office XP. Previous versions of Office have shared their title with their components, so that Office 97 contained Word 97, and Office 2000 contained Word 2000, but this no longer seems to be the case. So the current version may be referred to as Word 2002, Word 10, or Word XP. The first appears to be endorsed by Microsoft.
Mac OS X users currently have the Office X suite, which includes Word X, roughly equivalent to the 2002 (or XP) version on the PC. To further guard against confusion, Word X is also referred to as Word:mac by Microsoft.
Users of Pocket PCs are provided with Pocket Word, a portable version. I haven't been able to find any version information for this product, but it maintains compatibility with the current PC version.
It has always been possible to purchase Word separately from Office, and recent versions of Microsoft Works have also included Word - an improvement on Works' previous, less compatible bundled word processor.
At time of writing, Word 2003 is in the pipeline, and in keeping with recent developments in the Office suite focuses on DRM and networking features, alongside productivity enhancements.
Thanks to Servo5678 and Twinxor for extra info.