Most browsers have some mechanism to tune the maximum number of simultaneous connections to a web site. Firefox can easily be configured to open multiple simultaneous HTTP connections (extremetech, 2010). Internet Explorer has both an automated method and a registry hack available to achieve this functionality (Microsoft, 2010). I haven't figured out how to tune this property in Chrome yet but its default behavior is four simultaneous connections anyway (Sounders, 2008). Safari (which I do not currently use) and Opera (which I do occasionally) have the same default setting (Ibid.). Opera allows this parameter to be modified in Opera6.ini (Opera, 2010).
There aren't many disadvantages to the web browser for having multiple connections. As long as the client has CPU and bandwidth to make the requests and handle the resulting downloads the more connections it can open, the faster the surfing experience will be. One possible detriment, however, is if the web server identifies the activity as a Denial Of Service attack and drops or blocks the client (Ibid.), because multiple simultaneous connections may put a load on the server. Servers are, of course, designed to handle hundreds to millions of simultaneous requests. But if every client is opening numerous connections the load will be multiplied by a corresponding amount. Therefore it is sensible for the server or intervening hardware such as web accelerators and/or proxies to throttle sessions. As long as this doesn't actually cut off a client, however, it is probably in the client's (and their user's) best interest to have as many sessions open as possible. This is a parameter I do tune frequently if I'm using wget so I can visualize experiments that might prove how much of a benefit can be achieved before a server decides the activity is a DOS. But it's probably safe to assume that four is a perfectly reasonable number.
extremetech (2010) Hacking Firefox: Speed Up Your Browser [Online]. Available from: http://www.extremetech.com/article2/0,2845,1854196,00.asp (Accessed: 17 October, 2010)
Microsoft (2010) How do I configure Internet Explorer to download more than two files at one time? Available from: http://www.extremetech.com/article2/0,2845,1854196,00.asp (Accessed: 17 October, 2010)
Opera (2010) Opera's Settings File Explained [Online]. Available from: http://www.opera.com/support/usingopera/operaini/ (Accessed: 17 October, 2010)
Souders, S. (2008) Roundup on Parallel Connections [Online]. Available from: http://www.stevesouders.com/blog/2008/03/20/roundup-on-parallel-connections/ (Accessed: 17 October, 2010)