They have been successfully tested with Netscape Navigator v3.0, Communicator v4.0 and Microsoft Internet Explorer v3.0 on various platforms. Make sure you have Java enabled (Options->Network Preferences->Languages in Netscape).
Some users have experienced problems running Java applets from within corporate firewalls. Here is some advice from Travis Bryson of Sun:
By default, the Java runtime in Netscape 3.x tries to verify that a host has an IP address before it will download Java code from that host. In order to do this, it has to do a lookup for the host's name.
The problem with this scheme, for users within certain firewalls, is that their directory services are not set up to provide information about systems on the Internet external to the firewall. What this means is that, by default, they can't run many Java applets from outside their WAN.
In order to fix the problem here at Sun, I had to convert to configuring DNS lookups locally, AND configure my workstation to find the correct DNS server that could resolve IP addresses outside of Sun's WAN.