I'm quite sure Apparition is much slower than light speed. There's a passage in Price that seems to indicate that at least a few tenth of a second but possibly seconds pass during an Apparition. This is the wizard's subjective time, but I think it's roughly the same as the externally observed time.
Quoting Half-Blood Prince chapter 4, when Harry Apparates side-along with Dumbledore.
Harry felt Dumbledore's arm twist away from him and redoubled his grip: the next thing he knew, everything went black; he was being pressed very hard from all directions; he could not breathe, there were iron bands tightening around his chest; his eyeballs were being forced back into his head; his eardrums were being pushed deeper into his skull, and then–
He gulped great lungfuls of cold night air and opened his streaming eyes. He felt as though he had just been forced through a very tight rubber tube. […]
(Portkeys appear to work the same, because the books talk about similar sensations when wizards travel with them.)
Update: I found one more relevant quote, in Order of the Phoenix chapter 6.
Harry knew that Apparating was very difficult; it meant disappearing from one place and re-appearing almost instantly in another.
I take this as proof that Apparition is fast, but not as fast as the speed of light.