YUI:

XHR: yes
On success/failure, callback/pause (http://developer.yahoo.com/yui/connection/)

Timer/Timeout: yes

History/state: no
But it's in the "experimental" stage, beta testing should start in a month or so: http://developer.yahoo.com/yui/history/

Off-line Storage: no
no file export that I could easily find. No native cookie handler (but there are 3rd party ones).

Interaction with Desktop Apps:
Don't know

Extensibility:
Don't know

Animation: yes
At first glance, it looks pretty robust. Easing, relative movement, opacity, etc. (http://developer.yahoo.com/yui/animation/).

Number of items displayed: average
Current implementation is ok, scales well to reasonably sized things. Crazy things (which are more common in text analysis and rich prospect) are not so good now, but there is a widget in beta (http://developer.yahoo.com/yui/examples/datatable/index.html)that should improve things. Still not great.

Stateless messaging:

Usability: yes
Bookmarking no (but yes in the future using the in-development history widget). Layouts: good native layout management stuff (http://developer.yahoo.com/yui/grids/), cross-OS typography (http://developer.yahoo.com/yui/fonts/)and in the worst case, YUI components pay attention to css directives.

Browser Portability: yes
It's standards based, so "mostly". IE 6 and 7, Safari 2, Firefox 1.5 and 2, and Opera 9.(http://developer.yahoo.com/yui/articles/gbs/).

Start time: Good
Library files are many, but they are small. Boot up is fast.

Testing/debugging: yes
There is a great logger for watching the action of the AJAXy stuff, and Firebug.

HTML Portable: yes
It just creates AJAX that draws from libraries. As long as you've got the libraries, it'll work.

Remote Process Calls: yes
Data can be grabbed in HTML, JSON, XML, and text

Batch requests: yes
So it appears. I can't confirm on the official pages, but the community seems to have done it