JavaScript needs access to cookies if AJAX is used on a site with access restrictions based on cookies. Will HttpOnly cookies work on an AJAX site?
Edit: M
There's a bit more to this.
Ajax doesn't strictly require cookies, but they can be useful as other posters have mentioned. Marking a cookie HTTPOnly to hide it from scripts only partially works, because not all browsers support it, but also because there are common workarounds.
It's odd that the XMLHTTPresponse headers are giving the cookie, technically the server doesn't have to return the cookie with the response. Once it's set on the client, it stays set until it expires. Though there are schemes in which the cookie is changed with every request to prevent re-use. So you may be able to avoid that workaround by changing the server to not provide the cookie on the XMLHTTP responses.
In general though, I think HTTPOnly should be used with some caution. There are cross site scripting attacks where an attacker arranges for a user to submit an ajax-like request originating from another site, using simple post forms, without the use of XMLHTTP, and your browser's still-active cookie would authenticate the request.
If you want to be sure that an AJAX request is authenticated, the request itself AND the HTTP headers need to contain the cookie. Eg through the use of scripts or unique hidden inputs. HTTPOnly would hinder that.
Usually the interesting reason to want HTTPOnly is to prevent third-party content included on your webpage from stealing cookies. But there are many interesting reasons to be very cautious about including third-party content, and filter it aggressively.