To answer the original question, even if i'm a bit biased: Odyssey Web Browser (formerly known as OWB for MorphOS).
Because it's based on a recent WebKit and supports very well HTML5 standards (including HTML audio/video).
On a classic amiga, it would be of course very memory hungry, but not that slow, at least when disabling javascript. I think UAE users might find it interesting, if anyone was motivated enough to port it to OS3.x. Anyway, it's already ported to AROS/Zune (with serious limitations), so it might happen someday that it comes to 68k arch.
For those who don't know Odyssey because they don't own MorphOS or OS4 hardware (even if the version available on OS4 is quite old and incomplete), here are a couple old screenshots:
http://fabportnawak.free.fr/owbshots/ End of advertisement.
