Refreezing safe meat usually isn't a bacterial problem, it's a quality problem. I wouldn't refreeze two-day ground meat, though.

You'll have to cook it well done. Otherwise, the smell test is best. I'm voting for the choice that it'll be fine. Don't go by looks. It'll be gray due to oxidation.

If you didn't want to cook it as a burger, why not crumble it and make a bowl of chili or pasta sauce.

@greenstuff--yes, that surprised me, too.

According to the USDA site cited by drbabs:
"What is the best way to thaw ground beef?
The best way to safely thaw ground beef is in the refrigerator. Keeping meat cold while it is defrosting is essential to prevent growth of bacteria. Cook or refreeze within 1 or 2 days."
The reality is that it depends on the state that the beef was before it was frozen. If it was "on the edge," it may be over it in two days. But more likely, it's fine, and the Queen of Spoons taste test is the way to go.
I was pretty surprised that the USDA mentioned refreezing--that's something that I would absolutely not recommend.

I would probably use it--but as they say, when in doubt, throw it out. If it's a small portion, not much is being lost.

What would I do? Pull it out of the fridge and let it sit 5-10 minutes and give it a good deep sniff. I have a decent sense of smell, in the normal range I would guess, so if there was a hint of anything off, or sickly sweet, I'd toss it. If not, I'd cook it, but thoroughly -- not pink in the middle.

What should you do? If you want to be on the super safe side, go with the USDA sheet. Otherwise...use your nose.

I don't think so. The USDA says that after you defrost frozen ground beef, you should cook it immediately. Here's a link to info about ground beef and food safety:
http://www.fsis.usda.gov/factsheets/ground_beef_and_food_safety/index.asp

So, two days? As long as it's been refrigerated, and wrapped so it doesn't try out, sure.