Practically all major linux browsers support SSL and frames, konqueror and epiphany included.
I use Mozilla family browsers (firefox), and I've found
Natively, there are plugins for Java and Flash.
Some activex controls are vaguely supported - those that launch Windows media player can be made to launch mplayer - but all in all activex isn't supported as it's "a bad idea".
Shockwave support is unfortunately absent, unless you use Crossover Office