Despite the remarkable stabilty of Mozilla, I'd say if you're not a
webdesigner (me) or a techie (them) then you probably should hold off
investigating Mozilla and related technologies such as Netscape 6 for
a few more months. It has some strange hiccups which make it not so
fun to use, and currently the sole reason I use it is to find and
report those hiccups. Same for most people who use Mozilla.
But it's getting there, certainly.
(Note that by stability, I mean it doesn't crash while using it. But
it's still trying to wrap its mind around the concept of quitting
gracefully without having to be forceably kicked out of memory by the
OS)