Browsers
The implementation details are bound to be different for different browsers, browser versions or internet connection speeds (IE8 uses 2 connections on dial-up and up to 6 otherwise).
Also, these limits are usually user-configurable (i.e. network.http.max-connections-per-server in Mozilla) and one shouldn't assume specific values based on the browser version. The actual value might be accessible to a script though, such as window.maxConnectionsPerServer in IE.
But. does this limitation applies per tab, per browser instance or globally for all the instances of the browser?
The only relevant piece of information I found was this regarding IE (http://social.msdn.microsoft.com/Forums/ie/en-US/a46bb0ba-419d-43ec-ad1b-f9596d508ca3/simultaneous-http-connection-limit):
The connection limit is per process, the browser will make the determination about process creation as a web site owner you can't really change that. The process may be shared between multiple tabs/windows or it may not, it depends on many factors outside your control
More current data about browsers can be found at www.browserscope.org/?category=network
RFC
There is an updated draft which obsoletes RFC2616 (if approved).
Citing the relevant part (from https://datatracker.ietf.org/doc/html/draft-ietf-httpbis-p1-messaging-21#section-6.2.3):
6.2.3. Concurrency
Clients SHOULD limit the number of simultaneous connections that they
maintain to a given server.
Previous revisions of HTTP gave a specific number of connections as a
ceiling, but this was found to be impractical for many applications.
As a result, this specification does not mandate a particular maximum
number of connections, but instead encourages clients to be
conservative when opening multiple connections.
Multiple connections are typically used to avoid the "head-of-line
blocking" problem, wherein a request that takes significant server-
side processing and/or has a large payload blocks subsequent requests
on the same connection. However, each connection consumes server
resources. Furthermore, using multiple connections can cause
undesirable side effects in congested networks.
Note that servers might reject traffic that they deem abusive,
including an excessive number of connections from a client.