The functionality of Yahoo! Mail depends partly on your ISP. Some ISPs (like mine) pay Yahoo! to host their email, and so for people like me Yahoo! Mail is actually pretty decent, and works fairly well.
The rest of the world... well it varies depending on their mood I think.
I still use My Yahoo! as an RSS reader. It's handy to be able to jump between systems and keep all my feeds.
The Yahoo! Directory didn't used to be called that. When it started that was just Yahoo!
That was the whole website. Just categorized links. And it actually predated Alta Vista, although not by much and AV was always a much better way to find stuff than Yahoo! was.
Yahoo! did give Apache to the world though. I wonder how fast the web would have spread with just the NCSA junk for free server software.