I'm going to have to offer a different opinion than Chad, njam. There's nothing about tags that is intrinsically beneficial for SEO, and in fact misusing them can cause considerable SEO problems.
Bottom line, the primary purpose of tags is as an additional navigation tool for your visitors, and must be carefully implemented so not to damage your site's SEO. There's nothing magic about a tag - it's a link to your content organized in different ways
Tags are part of what's called your site's taxonomy - i.e. how it organizes its information. Tags allow the visitor to get listings of your existing content grouped by different topics - much like categories do, but on a more granular scale. And there's the kicker - tag listings are just your regular content, but grouped differently.
Because they're the same content as exists elsewhere on the site, they can easily be seen as duplicate content by the search engines, leading to a dilution of the ranking power of the actual posts. (This issue can also occur with category listings if they're not handled correctly, which is why you're already no-indexing them).
Most WordPress SEO specialists actually recommend that tag pages be no-indexed - a command that tells the search engines to not even include them in search results as they can so easily confuse the search engines about which version of your site's content is most important.
So... use tags on a website if you think they will significantly add to the visitors' ability to understand and navigate your site. Then, make sure you've taken steps to ensure they don't confuse the search engines.
Do NOT use tags just because they're available. If you don't have a clear strategy for using them, don't clutter your site with them.
If you want an idea of how tags fit into a taxonomy, here's a real-work analogy:
Think of your blog as a book on raising kids, for example. The book would have a bunch of separate chapters on things like childbirth, schooling and education, care and feeding, discipline, family finances - you get the drift.
These are the equivalent to your blog's categories - broad topics that would allow someone to pick up your book and leaf through it, immediately understanding what the book's about, and enabling them to read just the sections that apply to them.
In the back of the book is the index. It's full of words and phrases that you have used a couple times in the book, but aren't topics that deserve a whole chapter (category). These are the equivalent of your tags. For example, perhaps you mention peanut butter in the care & feeding chapter. Later, you also mention in the schooling chapter that parents shouldn't send peanut butter sandwiches in kids' lunches because of the allergy risk to others. In addition, you mention PB in passing in the finance chapter as a cheap source of protein for kids meals.
Obviously there'd be no point in having a whole chapter (category) on peanut butter, but a reader might find it useful to have the index (tags) at the back of the book show them all the places in your book you've mentioned peanut butter.
That's a bit of a facetious example, but hopefully it gives you an idea of the different uses? If not, lemme know and I'll try to clarify further. Just remember, there's nothing magic about tags for SEO and they in fact carry some risk. They are for human visitors. If the visitors don't find them useful, they shouldn't be there.
Paul