FeedRinse lets you combine and filter feeds, then export them for yourself or others to use as individual feeds or OPML feed bundles. It allows for fairly sophisticated filtering, but also has very simple tools which will fit most peoples' needs.
FreeMyFeed allows you to free your feed from authentication or invalid SSL certificates to get them into a reader. While the service does not store usernames and passwords on their server you are creating a new feed which gives unrestricted access to an otherwise protected feed so do not share the feed URLs.
Google FeedBurner allows you to publish feeds you've created for easy use by others. It also provides built-in usage statistics for your subscribers and tools to help you promote your feed. It has been a ubiquitous presence in the RSS world a long time, but seems to be less well supported recently - speculation is it may go the way of Google Reader.
FeedBlitz is a paid service which offers similar feed publishing and promotion tools to FeedBurner and much more. They focus heavily on marketing and social media in addition to basic feed management. They also have a detailed FeedBurner migration guide available.
MailChimp is an email newsletter publishing service that allows you to integrate feeds and customize the look and feel of your emails (unlike most publishing services). Its free for lists up to 2000 users.
Sometimes you want to get your updates via email - perhaps for a resource you don't use much, or when you can't use your reader, or as a way to have your Luddite friends stay in the RSS loop. If so you can try an RSS to email conversion service.
FeedMyInbox - allows up to 2 feeds for free or unlimited feeds for a monthly or annual fee. You get individual posts or digests nicely formatted with the original media like images embedded almost like they appear on a website.
Blogtrottr - a service that allows up to 25 subscriptions for free, as well as a paid Lite or Full service for up to 50 or unlimited feeds (respectively) and some extra features.
MailChimp is an email-based newsletter service which allows you to integrate RSS feeds (like from your blog) into your emails. A good solution for offering feeds or email from a single website.
"Feed43 engine converts free-form HTML or XML documents to valid RSS feeds by extracting snippets of text or HTML by means of applying search patterns, and then joining these snippets together using output templates to form user-friendly content of feed's items. The principle of extracting specific data from source documents is also known as “HTML scraping”"
Feed2js is a web-based service that allows you to parse RSS feeds and embed the results into your own web pages.
You can use the web-based service for free, or download and install a more full-featured PHP-based version to run on your own web site.
When you need something a little more powerful or flexible, try SimplePie. Installed on your web site, this PHP-based feed parser is both powerful and beginner-friendly.
Very flexible and customizable, SimplePie can probably meet all your RSS needs. We use it to power all the RSS functionality on the Ebling Library web site.