The gourmet food guides all say to finely strain the stock using increasingly smaller methods until you're pouring it through cheesecloth, but I have never understood why this would be beneficial unless you just want it to look pretty (i.e. clear).
I make stock regularly from bones, meat trimmings, and bags full of veggie scraps I've saved in my freezer. I never strain all the little bits out or skim the fat off the top. I think this stock is far more flavorful and satisfying than the premium stocks I used to buy. I use the stock as a base for many dishes and each batch is a little different depending on what types of meat and veggies I've had saved up but they all turn out great.
Most stock recipes say to cook everything for a couple hours, but there is amazing amount of flavor and nutrition still left in the ingredients, which is wasted if everything is tossed after just a few hours. Each of my "stock sessions" lasts about two days. I use a crockpot which has steady, gentle heat and doesn't need to be checked as often. About every 4-6 hours I pour some liquid off, package it for freezing, and then adding more water and sometimes more veggies and I continue gently cooking everything until the bones are soft and the marrow is dissolved. So in this way I'm making a rich bone broth, too, not just a simple stock. I generally get about 10 quarts from each "session" and I do this about once or twice a month or whenever I have enough scraps saved up.
Speaking of scraps ~ I save everything that I don't use in salads or recipes ~ onion skins, celery bottoms, mushroom stems, carrot tops, apple cores (seeds removed), cucumber peel, winter squash skins, etc. I've found there are only a few things that don't do well in a long-cooking stock, such as bell peppers and certain fruit bits, which get fed to the compost instead.