You can write Swing applets for IE 5 or NS 4.7 but you will have to use the plugin because those browsers' VM's don't support Swing. You can write Swing applets for NS 6 with no problem. To find out more about the plugin, visit Sun's plugin page.
The plugin is the correct answer. Seems like many developers don't want to hear this... i.e. see it as an extra step/hassle. We have used Swing on our intranet with Netscape 4.7 with good success as far as 'ease of use'. My only complaint with Swing is that it sometimes loads slow.
Swing works well using the Java plug-in as mentioned earlier. We user the plug-in supporting the 1.3 JRE and we think it is faster than the 1.2.2 (and more stable). If you have not used the plug-in before, beware that your web page must have a bunch of extra code in it (more than the simple APPLET tag). Sun's web site on the plug-in has some good examples. I've not had success with their HTML converter, but writing your own HTML is pretty straight forward.