I don't see any reason for immediate panic. For the most part, this makes man in the middle attacks easier, where someone pretends to be your normal internet connection. As long as you are on your home network and have reasonable security settings it should not be an issue.
Now, if you are out and about using free unprotected wi-fi networks, then it's riskier. But it's not a new risk. It's never been a good idea to go to a sensitive website on an open wi-fi network. This vulnerability just make it a bit easier. When it works it does not remove encryption, but it does trick your system into using older less sophisticated encryption. Encryption that is possible to break without resorting to super computers.
It's unclear (to me) if this would affect VPN connections as well; the usual way of dealing with open networks and security. So even if you have a VPN you might want to avoid using open wi-fi until this is patched in Safari, or your VPN provider announces that they are not vulnerable.
Anyway, Apple said they will have a patch out within a week. That's pretty fast for them. They are obviously taking it seriously.
Of course, as the story progresses it may turn out I'm underacting.