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I see methods for subscribing to new comments on an entry and new posts in a forum topic ...

But what I really want to know is: how do I provide an e-mail subscription option for new entries in each category (or a tag)?

Use feedburner, it provides loads of options. google it.

I use and like FeedBurner.

But I use it for overall blog feeds. Not for updates on individual pages. In order words, I envision a different RSS feed for every page, category, and tag.

Let me look further ...

EE is flexible enough to let you create indivual feeds for that. On one of my sites, I have feeds for every article (think comments), so based on categories should be easy.

I can make the feeds. What I want is the ability for members to also subscribe via e-mail.

Can you point me to a thread on that?

There is no such functionality built-in into EE, although it might be possible to do with an extension.

Thank you. That is good to know.