Theoretically, a limit of two connections per hostname is suggested by HTTP/1.1.
See HTTP/1.1 - RFC 2616, section 8.1.4 "Connections - Practical consideration"
A single-user client SHOULD NOT maintain more than 2 connections with any server or proxy.
Generally speaking, browsers open between 6 and 8 connections per server.
For example:
- IE8 uses 6 connections
- Firefox 3 uses 6 connections
It is also possible to reconfigure the browser to use different limits.
See also browserscope or Steve Souders' Roundup on Parallel Connections.