It's not very useful to me.
When I'm learning anything visual (GUI, plotting libraries) I really like a gallery of live examples.
YUI's site seems to assume that you already know what you are looking for.
The new site puts 4 examples (todo, calendar, charts, and search) on the home page, which is 4 more than I found the last time I looked. For contrast, jQuery UI has dozens of examples (under http://jqueryui.com/demos).
You have the pages - http://yuilibrary.com/yui/docs/examples/, but it's not really promoted. I bet you don't get many clicks to that page (due to the design of your site pushing people to other sections), but I bet the people who go there find it useful. Everyone else lands here: http://yuilibrary.com/yui/docs/guides/. Unless they think to go back, everywhere they click will look like a man page, complete with big "caveat" boxes. Functional, if you are debugging YUI, but otherwise it's just ugly.
IMO, you should promote the live examples more, rather than the API docs. If I want to do some complex stuff, I'll look for a section labeled "API". If I'm just trying to assess whether a toolkit is useful, if I don't stumble onto live examples I'll wonder why you aren't even using the tookit on its own homepage.
You could also go one better, and put some screenshots (or inlined examples) on the example index docs/examples/.
People don't complain about "design" because they think it's ugly. They complain because they can't find what they are looking for (even if they don't know what they want).