RSS stands for Real Simple Syndication. Syndication of a feed would seem to mean the ability to republish that feed on another website. Isn’t that what syndication is after all? For the most part, people “syndicate” feeds within their own personal RSS Readers. So by and large people syndicate for personal use. However, republishing on a website is a totally different story. Oddly enough, feed providers (both small (most blogs) and very large (Yahoo News)) have very vague Terms of Service when it comes to the use of a feed. Often, the terms are contradictory. I have emailed several large feed providers to have them clarify their terms.
On my own site, I have republished feeds from other sites. I have written to all of them for permission. This is at the least, one means of protecting oneself. If in doubt, ask. I have found a couple examples of explicit statements regarding the republishing of feeds