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.
The network results at Browserscope will give you both Connections per Hostname and Max Connections for popular browsers. The data is gathered by running tests on users "in the wild," so it will stay up to date.