In Firefox 3, the answer is 6 per domain: as soon as a 7th XmlHttpRequest (on any tab) to the same domain is fired, it is queued until one of the other 6 finish.
What are the numbers for the other major browsers?
Also, are there ways around these limits without having my users modify their browser settings? For example, are there limits to the number of jsonp requests (which use script tag injection rather than an XmlHttpRequest object)?
Background: My users can make XmlHttpRequests from a web page to the server, asking the server to run ssh commands on remote hosts. If the remote hosts are down, the ssh command takes a few minutes to fail, eventually preventing my users from performing any further commands.