Is it legal to refuse customer's request for refunding unused portion of subscription of service?
About 14 months ago, I intentionally subscripted to Yahoo real time quote service for one year, but unintentionally to "agree" with their refund policy and automatic annual subscription renewal.

I have not read their agreement policy but if you opted out rather than them banning you I don't think there is any way you can get a refund. When you sign a cell phone contract they hold you to the full term. I am sure that is what Yahoo requires.
The only way I can see that you ''unintentionally'' ''agreed'' is if you didn't read the agreement and automatically clicked 'agree' which is not an out for you.
I am not sure about the renewal policy but I really don't see how they can hold you responsible to renew something you decided you do not want and you no longer have.
Did you cancel because you were not satisfied or simply because you no longer wanted the service for whatever reasons?

You are locked into their terms of service, so what ever their policy is, that is what you are stuck with