Showdown has been tested successfully with:
Firefox 1.5 and 2.0
Chrome 12.0
Internet Explorer 6 and 7
Safari 2.0.4
Opera 8.54 and 9.10
Netscape 8.1.2
Konqueror 3.5.4
Generally, Showdown should work in any browser that supports ECMA 262 3rd Edition (JavaScript 1.5).
The converter might even work in things that aren't web browsers, like Acrobat. However, no promises.
Showdown is intended to work on any supported Node.js version (see the Node.js releases schedule.
Previous versions may also be supported, but no accomodations are made to ensure this.