Assuming you're talking about the Yahoo! News RSS feeds, if you look at Yahoo's terms on their RSS page, they don't require you to post a copyright notice, but they do want you to say "Yahoo! News" or use their logo.
Yahoo! aggregates content, but they license it: they sign licensing agreements and pay AP, Reuters, and all the other providers. So they have a pretty good case for saying that their compilation is subject to copyright (in the same way that a local newspaper can still be copyright even if it includes wire service stories).
Here's what I don't get: if the use is personal (i.e. a page that only I read), then who reads the attribution? Me? When I read this before I thought it said "personal *or* non-commercial use", then the attribution statement makes more sense.
Yes, you certainly could use it on a page where you were the only user. I am not Yahoo's lawyer, but I would be really, really, really surprised if they would care about any non-commercial usage, even if other people used it than just yourself.
That would just be dumb to put out an RSS feed and not allow for non-commercial usage -- and Yahoo has not been dumb lately.