When making chili in the crockpot, must the ground beef or turkey be precooked, or can I just throw everything in and cook it all day?
There are two different issues: safety, and flavor.
From a safety point of view, assuming you don't overload your slow cooker, and it comes up to safe temperatures (140 F, 60 C) in less than two hours (preferably much less), it is perfectly safe to begin cooking in a slow cooker with raw ground meat.
On the other hand, you will not get the flavor development that browning meat provides. Slow cookers are essentially appliances for the long, slow, moist cooking method calling braising.
Many conventional (stovetop and oven) braising recipes begin by searing or browning the meat, prior to the braising phase. This develops deeper, richer flavors due to the maillard reaction.
If you skip this step for a slow cooker, you will lose the benefit of this flavor development. In some recipes, this may not be an issue, or it may even be traditional (such as for Cincinnati style chili). For other recipes, including many chili recipes, you may choose to brown or sear your meat (or other ingredients) prior to adding it to the slow cooker to benefit from the flavor development; in this case, it is not necessary to cook the food all the way through—that will happen in the slow cooker.
You certainly can add raw ground beef to the crockpot. As a matter of fact, many (if not most) slow-cooker chili recipes ask for the meat to be added raw. The whole purpose of a slow-cooker is to save effort on the part of the cook/dishwasher. Browning the meat ahead of time requires effort and a whole additional pot to wash.