how to detect available RSS feeds on a web page?

In Firefox (at least my Firefox 21), you can go into Page Info and Feeds. I'm pretty sure this is independent of any add-ons; I got so fed up with having to do that all the time that I hunted down and installed the RSS Icon In Awesomebar add-on. It's a little less un-awesome now. There appears to be a few alternative implementations available.

For Chrome, there is a handy extension from Google called RSS Subscription Extension. It puts the standard RSS icon in the search bar if it detects the page has an RSS feed.

As of 2019, the Feed Indicator extension for Firefox adds back an RSS icon in the address bar for websites that have RSS/Atom feeds.