Do any iOS versions come with a built-in RSS reader?
Sort of... you can go into Safari, choose a website, then click the bookmark icon, select the @ tab, click Subscriptions and then click Add Current Site.
Otherwise Reeder for IOS is a great RSS reader. https://itunes.apple.com/us/app/reeder-2/id697846300?ls=1&mt=8
You could use Reading List on Safari. It's syncs automatically between all your iDevices. Reading List feature has been available on iOS since the launch of iOS 7. Some apps like TweetBot allow you to directly send links to the Reading List which you can catch up later.