For MorphOS there's Sputnik, which performs not too shabby. It's even able to annoy you with slow moving dynamic html ads where you always have to carefully spot for the close gadget...
Of course Opera is still lightyears ahead, but Marcik did a great job with Sputnik so far and he hasn't abandoned yet, so there's more to expect. There's also a bounty for Sputnik on OS4, about a port to AROS or 68k I don't know the plans.