It started with an Eevee tweet:

like does anyone actually care about blog categories, considering you can just skim the list of titles and get a pretty good idea

It turns out that I have opinions on this, perhaps unsurprisingly. My answer is 'yes', or at least potentially yes. In fact I think there are several different levels of things that you want to have in a fully featured blog system.

The pragmatic purpose of categories is to allow people to easily follow only a subset of your blog, both through syndication feeds and perhaps other mechanisms. The more disparate the subjects you cover in your blog, the more likely people are to want a way to follow a subset of it; conversely, if you already have a narrow focus there may be no point in trying to subdivide it. Here on Wandering Thoughts I definitely have feed readers fetching category feeds for several of my categories. Of course you can choose not to provide this sort of thing in the interest of broadening the minds of your readers, but this may well cost you readers.

(Some form of restricted scope feeds are also handy if you think you may someday want to feed selected entries to, say, a specific planet-style aggregator. The importance of this depends on how many of your entries would be irrelevant to a particular aggregator; for example, I'd definitely want a category for Go if I ever wanted to be part of a hypothetical 'Planet Go'.)

Relatively broad topics are there so that readers can easily find more of your writing on specific areas of interest to them. This is the domain of 'that entry on ZFS was useful, has she written more about it?', where a reader is expanding outwards from some initial entry they've landed on. My view is that topics are less predictable and more retrospective than categories; they sort of emerge organically from your writing as you find you've written a bunch about a specific area.

(You might as well provide syndication feeds for topics too if you can support it easily, but I think it's less important than with categories. Among other things, your writing on any particular topic may be extremely sporadic or even stop.)

Finally, I definitely feel that real blog usability means that you want some mechanism that will let you create a collection of direct and visible links for things like '(strongly) related entries', 'next/previous entry in this series of entries', and the like. I don't think tags (as conventionally implemented) are the right answer for this because they're not clear enough (I discussed this in my thoughts on tags for blog entries). These sort of strong relationships between entries are your best hooks for getting new visitors to read more, so you want them and their relevance to be clearly visible in ways that you wouldn't do for categories and topics.

(For instance, for 'next/previous in series' I think you should not just mention that here's where a reader finds more but also show the entry titles.)

I've wound up feeling that to the extent that you have tags as such, they're an implementation detail that may be used to create any or all of the above. This means that your tags may be namespaced into some structured namespaces, and tags in these namespaces may be presented separately from each other (and perhaps in different ways). The sorts of namespaces you want for tags may vary between different blogs, depending on what the blog is used to write about.

(For instance, consider a blog that's used to write about TV series. You're going to want a way to clearly tie all entries that cover a specific series together and you probably want it to be clear to readers and distinct from how they find all your writing about, say, one director or writer. So you probably want not just a big generic 'Tags: ...' thing that smashes all of these separate namespaces together but instead specific 'Series: ...' and so on, and then maybe a 'Tags: ...' as well.)