Ground beef goes bad really quickly. The reason for that is that grinding it exposes vastly more surface area of the meat to oxygen, as compared with a steak. And oxygen is one of the primary sources of sustenance for the tiny bacteria that cause food poisoning.
(Protein is another — which is why meat is so much more perishable than fruits or vegetables.)
Not only that, but the structure of the ground meat basically forms a multitude of little air pockets all throughout the meat; and each one of these little pockets is a breeding ground for bacteria.
A steak is a solid slab of meat, and its interior is essentially sterile: no oxygen can get to to it, which means bacteria won't grow there.
The surface of a steak is another matter. Bacteria can grow on the surface, but fortunately, when you cook a steak, it's the surface that's in contact with the hot pan or grill. And heat is one of the most surefire ways of eradicating those bacteria. Most of them perish instantly at about 160°F, and of course grilling a steak uses temperatures far higher than that.
Thus a steak is pretty safe to keep in your fridge for a couple of days. (Also see: How to Cook a Steak Without Poisoning Someone)
Bacteria: Contamination Vs. Spoilage
I mentioned food poisoning a moment ago, but food poisoning and food spoilage are two separate things. Spoilage is also caused by bacteria, but not the ones, like salmonella or e. coli (which is sometimes referred to as the "hamburger disease"), that cause food poisoning.
We'll call that contamination. One of the characteristics (or non-characteristics, if you prefer) of contaminated food, is that it displays no signs of having been contaminated. No off smells or texture changes or discoloration. A deadly burger can appear, and in fact be, perfectly "fresh."
Food spoilage, on the other hand, is simply an umbrella term for the various signs that communicate to your senses of smell, sight, or touch, that you hadn't better eat that food.
Like contamination, spoilage is also caused by bacteria, but the bacteria that cause spoilage don't actually make you sick. This is largely because most of us won't eat food that smells bad or feels slimy, but even if we did, the worst that would happen is that it would taste and smell gross.
In other words, spoilage is a function of freshness (or lack thereof), whereas contamination (i.e. food that is tainted by the kinds of pathogens that can make you sick) can occur even in foods that are otherwise "fresh."
Having said that, if your ground beef is contaminated with a pathogen, and then you let it sit in the fridge until it starts to exhibit signs of spoilage, the pathogens will have multiplied along with the spoilage bacteria.
Is Your Ground Beef Spoiled?
In the case of ground beef, what signs (if any) you'll detect will depend on how badly spoiled it is. If it feels slimy, it's starting to go bad. The slime on the surface is caused by the buildup of bacterial cells —it's the little critters' actual bodies (such as they are).
Next there's smell — if it smells funky, it's spoiled. The smell is caused by the gases produced by the bacteria.
Oddly enough, despite the smell and slime, the protein of the meat remains unchanged, thus it is every bit as nutritious.
Finally, ground beef can change color when it spoils, going from the familiar rust-red color (produced by iron — the same ingredient that gives blood its color) to a flat gray color as the bacteria break down the iron compounds in the meat.
So in short, if your ground beef is gray, slimy or smelly, it's spoiled.
Interestingly enough, there is a theory that the odor bacteria produce is an adaptive technique that evolved as a way of discouraging other organisms (e.g. people) from competing with them for their food supply. In other words, if we smell funky food, we'll keep moving, leaving the bacteria free to have their way with it.
Keeping Ground Beef Fresh
I hate to waste food, so I'm pretty draconian with the ground beef I buy at the store. No matter what, ground beef requires you to take some action on the first day: either cook it or freeze it.
We eat quite a few burgers at my house, especially during the summer when I like to cook them outside on the grill. So when it's on sale, I buy a bunch of it.
Usually you'll see a sell-by date on the package, and even if that date is two or three days in the future, pay no attention to it. Either cook it the day you bring it home, or freeze it. (Freezing, I should note, does not kill the bacteria that cause spoilage or food poisoning, but it does slow down their reproductive cycle. They go into a state of suspended animation.)
What I do is season the meat and form it into patties, then transfer the patties to freezer bags and freeze them. If you have the foresight to know the night before that you want to have burgers the following night, you can thaw them overnight in the refrigerator. If you have no foresight, you can do what I do, which is to thaw them by placing the baggie in a casserole dish in the sink and run cold water over it so that the burgers are submerged and there is a constant flow of cold running water.
NOTE: It has to be cold water. If you use hot or even warm water, you could absolutely give yourself food poisoning.
Fortunately, even if you only manage to thaw them partway, you can still cook them. Here's my guide to cooking the most amazing hamburgers.