Any browser that can be configured to use a proxy, which should be virtually all browsers, including Firefox, Internet Explorer, Opera, and Safari among others. Direct browser support is not an absolute requirement since Privoxy runs as a separate application and talks to the browser in the standardized HTTP protocol, just like a web server does.
At present, Privoxy is known to run on Windows 95 and later versions (98, ME, 2000, XP, Vista, Windows 7 etc.), GNU/Linux (RedHat, SuSE, Debian, Fedora, Gentoo, Slackware and others), Mac OS X (10.4 and upwards on PPC and Intel processors), OS/2, Haiku, DragonFly, FreeBSD, NetBSD, OpenBSD, Solaris, and various other flavors of Unix.
Privoxy used to work on AmigaOS and QNX, too, but the code currently isn't maintained and its status unknown. It might no longer compile, but getting it working again shouldn't be too hard.
But any operating system that runs TCP/IP, can conceivably take advantage of Privoxy in a networked situation where Privoxy would run as a server on a LAN gateway. Then only the "gateway" needs to be running one of the above operating systems.
Source code is freely available, so porting to other operating systems is always a possibility.
As long as there is some way to set a HTTP proxy for the client, then yes, any application can be used, whether it is strictly speaking a "browser" or not. Though this may not be the best approach for dealing with some of the common abuses of HTML in email. See How can I configure Privoxy with Outlook? below for more on this.
Be aware that HTML email presents a number of unique security and privacy related issues, that can require advanced skills to overcome. The developers recommend using email clients that can be configured to convert HTML to plain text for these reasons.
All browsers should be told to use Privoxy as a proxy by specifying the correct proxy address and port number in the appropriate configuration area for the browser. It's possible to combine Privoxy with a packet filter to intercept HTTP requests even if the client isn't explicitly configured to use Privoxy, but where possible, configuring the client is recommended. See the User Manual for more details. You should also flush your browser's memory and disk cache to get rid of any cached junk items, and remove any stored cookies.
If you set up the Privoxy to run on the computer you browse from (rather than your ISP's server or some networked computer on a LAN), the proxy will be on 127.0.0.1 (sometimes referred to as "localhost", which is the special name used by every computer on the Internet to refer to itself) and the port will be 8118 (unless you used the listen-address config option to tell Privoxy to run on a different port).
When configuring your browser's proxy settings you typically enter the word "localhost" or the IP address "127.0.0.1" in the boxes next to "HTTP" and "Secure" (HTTPS) and then the number "8118" for "port". This tells your browser to send all web requests to Privoxy instead of directly to the Internet.
Privoxy can also be used to proxy for a Local Area Network. In this case, your would enter either the IP address of the LAN host where Privoxy is running, or the equivalent hostname, e.g. 192.168.1.1. Port assignment would be same as above. Note that Privoxy doesn't listen on any LAN interfaces by default.
Privoxy does not currently handle any other protocols such as FTP, SMTP, IM, IRC, ICQ, etc.
Did you configure your browser to use Privoxy as a proxy? It does not sound like it. See above. You might also try flushing the browser's caches to force a full re-reading of pages. You can verify that Privoxy is running, and your browser is correctly configured by entering the special URL: http://p.p/. This should take you to a page titled "This is Privoxy.." with access to Privoxy's internal configuration. If you see this, then you are good to go. If you receive a page saying "Privoxy is not running", then the browser is not set up to use your Privoxy installation. If you receive anything else (probably nothing at all), it could either be that the browser is not set up correctly, or that Privoxy is not running at all. Check the log file. For instructions on starting Privoxy and browser configuration, see the chapter on starting Privoxy in the User Manual.
Now if http://p.p/ works for you, but other parts of Privoxy's web interface show the dummy page, your browser has cached a redirection it encountered before Privoxy was being used. You need to clear your browser's cache. Note that shift-reloading the dummy page won't help, since that'll only refresh the dummy page, not the redirection that lead you there.
The procedure for clearing the cache varies from browser to browser. For example, Mozilla/Netscape users would click Edit --> Preferences --> Advanced --> Cache and then click both "Clear Memory Cache" and "Clear Disk Cache". In some Firefox versions it's Tools --> Options --> Privacy --> Cache and then click "Clear Cache Now".