My 2 cents...

Categories are drawers. And in your drawers you have files. Categories should rarely change.

Tags on the other hand are like post-its. You could even say they are ephemeral. Use them as a way to organize content based on less important factors or based on trends. Or when you need to organize content that hierarchically is inside very different categories.

Let me give you a practical example.

A website that covers news for motorcycles is struggling to organize its content so that menus are simple for users to navigate, yet information can easily be filtered. Such a website would cover news for brands, races & tournaments, travel guides, motorcycling accessories etc. etc.

The dumb approach would be to create a category per motorcycle brand in order to add more categories in it to cover news, races, pricing etc. The smart way would be to create the categories that actually matter: news, races/tournamenents, travel guides, accessories etc. Instead of making motorcycle brands as categories, convert them (or start using them) as tags. So if I need to add a travel guide with a KTM, Ducati and BMW touring motorcycles, I categorize the item under "travel guides" and add 3 tags for each brand. This way a user can instantly filter e.g. all items associated with "Ducati".

You may be thinking that tags may get out of hand, or that you can't filter them. That's wrong. First off, you can create direct menu links to tags if you want to. So you could make a "Motorcycle Brands" menu with K2 tags in it. And you could even filter from which categories to display items that have each tag referenced (in order to create separate menus for news, travel guides etc.). And what about tags getting out of hand. Now, this is where K2 shines and why Joomla's content is 10 years back. K2 (under Settings >> Advanced (tab)) allows for rules to be placed when entering tags (e.g. change the tag characters case or transliterate to latin). Hell, you can even predefine your tags and prevent editors from creating their own (e.g. on a sports news site, team names could be tags).

See: jmp.sh/gcsEnVG

Of course these examples can easily be expanded to other use cases. E.g. product websites, corporate websites etc. It really is a matter of properly orchestrating your content. And K2 provides you the tools to do that since the day it was launched.

That being said, if you ever stumble on the 3% that doesn't fit what K2 provides out of the box, you can always use the awesome third-party K2 extensions from the likes of web357.com (Multiple Categories for K2) and joomreem.com & joomcar.net (for filters/search/sorting etc.) - just to name a few...

In any case, we're always here to help :)