Our current science believes that nothing is faster than the speed of light, so the answer to your question would be "no".
(Sun rays are nothing but electromagnetic radiation which travels at the speed of light)
yes, the universe itself. As far as we know, there's no limit to how fast the universe itself can expand (pretty sure a moderator said as much in a different, earlier topic), and we're already pretty content with the idea that the volume of space is limitless (as opposed to being 26.5+ billion years across).
Also, if that new cosmic wave story about pulsars is accepted (to me, it looks like a mighty big if), that would open up at least a second thing if not a whole series of things that is in the realm of FTL. If I understand the story correctly, only energy and mass are limited by c. Anything that "creates" energy or mass or drives interaction between the two wouldn't be.
Coming up with all this cool stuff we can't even begin to test yet makes me think it's so depressing to realize I'm probably going to be riding Earth crust down into the hellish goo of the mantle long before any cool practical demonstrations of these theories comes about.
I just finished reading Phil Plait's "Death From the Skies". In the last chapter, he talks about how the universe will end. One part is about how the expansion of the universe will accelerate until it exceeds the speed of light. At that point, though the Universe is continuing to expand at an ever greater rate, the *observable* portion of it will contract as more and more objects slip beyond the observable horizon, as the expansion means that their light can never reach us. He talked briefly about the sort of civilization that could grow up, eeking out an existence near the end of the age of stars (before fusion becomes impossible for all stars), unable to see anything beyond our galaxy, which would itself be very dim by that time, dominated by red dwarf stars.
The one problem I've always had with various predictions about the end of the universe, is that they take the currently observed trends, and just extrapolate them forward.
Even within BB theory we know expansion isn't constant, and has actually sped up drastically, then slowed drastically, at least once before (the inflationary epoch). As such it's quite possible the universe won't end a cold sparse wasteland...
It's really hard to tell at this point what is going to happen when we don't really understand the mechanism behind the trends we see.