IcedTea's plugin is worthless. It doesn't deal with signed applets.
The only two things I use java for with a web browser are two different types of network kvm. One uses a java applet, and the other uses a java webstart application. I had to use 32bit sun java to get support for both at once.
Now the only thing left 32bit is mplayer for win32 codecs. I will have to do much testing and see if I can now live without them and use mplayer.x86_64. If so I can pretty much go pure 64bit. I do run into x86_64 applications every so often that don't behave properly. The last example I can think of is rtorrent.