This question has been asked to me a lot of times. Sometimes though, myself included, accumulate a lot of accounts at Yahoo! from their email service to their chat messenger, including their various services.

Back then I was having trouble deleting and closing my Yahoo account from Yahoo! So I copied the link to their account deletion page so that I have easy access to it.

So to delete or close your Yahoo account, just visit this URL:
https://edit.yahoo.com/config/delete_user

Before logging in (and to prevent phishing), verify and make sure the link is right. It should be pointing to yahoo.com and uses secure protocol (https://)

For more info regarding deletion of your Yahoo account, just visit their help page.