Making Beef Stew: What are the pros and cons of browning beet in seasoned flour or not?

It's not necessary to flour the meat. But searing the beef cubes and then deglazing the pan with some wine, water or stock will create a "fond" that adds great flavor to your stew. For example, see step #4 in this Julia Child beef stew recipe:
http://www.foodandwine.com/recipes/my-best-beef-stew

I always dust in flour (with seasoning) and brown the meat. I feel that it gives more depth to the flavor and also helps the meat not become mush after being in the pot for a few hours. It also thickens the gravy.

I used to flour my beef and then brown. Then Cooks Illustrated suggested not using the flour as it actually prevents the meat itself from browning. Then, my slow cooker recipe (Slow Cooker Revolution) called for not browning the meat at all. I was doubtful, but it was delicious!

I rarely brown the meat for a stew, and never seem to have any problem with the sauce thickening. Just salt and pepper, and any other seasonings you like.

Anywhere I can cut refined flour without much notice I do....that being said the flour does help thicken the stew, but I usually skip it, I still season with salt, pepper, and garlic though.

My preference when making beef stew is to cut the meat in uniform pieces, taking out gristle and taking off too much fat. Then I toss the meat in seasoned flour and brown and put in a separate bowl. I use the pan with the drippings to sauté onions and garlic, and that is the base for the stew. The drippings not only have great flavor, they thicken the stew. I add everything together and add vegetables and put the mixture in the oven at about 250.