igvita.com explains what SPDY is, how it works and where it is used. As you may remember, Google proposed an add-on to HTTP that was faster because of multiplexing, server pushing and better compression including compression of headers and the use of a pre-defined dictionary.
I heard about SPDY when Google announced it in 2009 but hadn’t heard much since. For all I knew it was something that never took off like Google Go. But it turns out that Google has been serving pages in SPDY to Chrome for several months now. As you use Chrome you may notice that unlike other browsers chrome does not display “http://” at the beginning of the location bar. Part of the reason is because Gmail, Google Docs and other Google services are actually running on “spdy://”. So you don’t even know it: you are using SPDY.
There is a ticket filed for Firefox but it doesn’t look like SPDY will be implemented anytime soon. I couldn’t find anything about plans for SPDY for Safari or Internet Explorer.
UPDATE (2 April 2012): Firefox 11 implements SPDY as an option (search for “spdy” on about:config), and according to this Mazillazine thread, Firefox 13 will enable SPDY by default. That thread also mentions an add-on that shows an icon when a site is using SPDY (Search for “spdy” on addons.mozilla.org).