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Putting aside the question of whether or not feed readers are still popular, I kinda thought that RSS is a format that has several applications, with readers being only one example. Is that true or not?
Sorry to post such an elementary question... but I did Google(TM) this to death and couldn't find a solid answer.
"Oh I hear people don't even use news readers anymore..."
RSS feeds can be aggregated in a number of ways, aside from the basic feed reader. Feeds are often added to websites and are a great way to syndicate your content. One common example today is when people add your feed content to their start pages like Yahoo and iGoogle pages.
When you syndicate that content out you will get links back to the original. That's a big motivator for some.
Also, keep in mind that not everyone wants to visit your site on a daily basis to see if there's anything new. Savvy customers will subscribe to several feeds and monitor you and your competitors. If you don't have a feed you're missing out on a wider audience.
Don't think of RSS as simply something to be viewed in a feed reader. It has wider use than just that.