To answer the thread topic's question, I'd have to say that probably half of the remixes I enjoy the most, I've never heard the original source material. It's always interesting to hear the original of course, but I enjoy a great many of these remixes as musical tracks unto themselves.
That being said, I think the remixes that top my list of favorites are those which I am familiar with the original source tune. So it's a mixed bag of sorts.
Now, another issue altogether is whether or not I've actually played the game. I'd have to say that 95% of the remixes I enjoy, I've never played the game the source material is from. A ready example that comes to mind is Final Fantasy VII - never played the game, but I have the soundtrack and VotL is probably my favorite OCR tribute album to date. Go figure!