I've found it really difficult to find good, responsible news reports on this event. I'm sure Steve Gibson (grc.com) will report on it on this week's upcoming Security Now.
Here's a pretty good article on this event at Cnet.
In this case, you're password would only have been compromised if you'd logged into the Yahoo Contributor Network, apparently also known as Yahoo Voices, and previous to Yahoo, Associated Content which Yahoo acquired.
Here's the main, important advice which has been true for a long time, maybe always. Please don't use the same password for more than one site. I like the recommendation to use LastPass at lastpass.com. It gives you a secure way to keep up with and use your passwords.
The only reason you need to change your password on other sites than Yahoo is if you (ever) used the same passwords on them.