@Karen

The first such plugin that I have retrieved from my archive is Media Library Categories, by Hart Associates.

To get that link into the WordPress Extend directory, I searched in Admin; clicking Plugins, then Add New, then typing 'media categories'. There are 'a number' of very similar titles (263 total returns, tho they will soon include off-topic items).

I then modified the search-term to 'media tags', and at the top of the list of 540 returns are 2 titled "Media Tags". (Images are of course refered to as "Media"...)

To minimize the likelihood that future WordPress changes might bring heartbreak & anguish to someone who builds an edifice on top of options or facilities provided by 3rd-party plugins, try to pick from titles that are popular with others, and seem to be well-used (or that are very close to what WordPress itself does, anyway). WP will try to avoid leaving such installed user bases 'in the lurch', as will an involved & active plugin-author.

Likewise, try to avoid 'too-clever' or 'unusual' or proprietary approaches which WordPress will feel less obliged to support or avoid 'breaking'.

Be cautious. Move slowly. Do your homework, first. This is one of those areas or fields where it is said: "Fools rush in where angels fear to tread". :)

Good luck!