Cooked bones are quite dangerous. Cooking changes the structure of the bone, making it indigestible and easily splinterable. Raw bones rarely splinter and are fully digestible, even the collagen proteins that some people claim are "indigestible." It is mostly the byproducts of the digested bone that form the bulk of a raw-fed animal's feces. Dogs and cats do not need the fiber from grains and vegetables, and feeding such foods only results in the big, soft, malodorous stools everyone complains about.
Let me repeat this for good measure: raw bones are completely digestible and are not dangerous for your animal. They are no more dangerous than kibble, and the only reasons they are made out to be dangerous are a) people misunderstand that raw bones are fully digestible while cooked are not, b) people want to scare you into thinking you are going to kill your dog if you give them bones, and c) bone-induced problems are blown way out of proportion in an effort to maintain the status quo of feeding kibble. What these people forget to tell you about are the 60,000 dogs suffering from bloat each year—of which nearly 20,000 die (Burrows, C.F. and L.A. Ignaszewski. 1990. Canine gastric dilatation-volvulus. Journal of Small Animal Practice. 35:295-298. In Lonsdale, T. 2001. Raw Meaty Bones. pg 117)—or the number of dogs dying from choking on kibble—which is a more common occurrence than one hears of! They also forget to mention the numbers of dogs that choked on or swallowed tennis balls, rocks, sticks, and a variety of other objects. These incidences FAR outweigh the numbers of dogs that have problems with raw bones. Just take a survey of veterinarians in your area and see what the most common blockage or choking culprits are in their specific practices. Do not forget to ask how many dogs they have treated (successfully and unsuccessfully) for bloat.
Yes, problems can occur with raw bones, just as problems can occur with feeding the "safer" kibble (bloat, choking, telescoping bowel, aspirated kibble leading to pneumonia, etc.). These problems typically occur in dogs that gulp their food or are fed small things like chicken wings and necks (the prime suspects of choking incidences on raw). Other culprits are the large weight-bearing bones of herbivores, things like knuckle bones, femurs, etc. These, ironically, are the kinds of bones pet food manufacturers and some vets recommend dogs receive regularly to help keep teeth clean! These bones chip or break teeth and can have pieces of bone flake off.
If you are concerned about choking or about bones getting stuck or about broken teeth, here are some things you can do:
Feed appropriately sized pieces. Do not be feeding a dog the size of a Rottweiler a little chicken neck or wing! Feed that dog a whole chicken. Bigger pieces force the dog to slow down and chew. Also, stay away from cut bones; this includes things like cut up neck bones (where they are cut into individual vertebrae), cut ox-tail bones, and cut knuckle bones. The smaller size encourages inappropriate gulping, not to mention the rather sharp edges left over from the saw blade! Feed large MEATY bones that are in as whole condition as possible.
Feed raw meaty bones frozen or partially frozen. The dog will have to work at it much harder and will be forced to slow down.
Do not feed the big weight-bearing bones of large herbivores. These are well-known for chipping and cracking teeth! These include the ever popular "recreational bones" like cow femurs and soup bones. They are incredibly dense and hard, and can result in slab fractures and cracked carnassial teeth. Avoid them if you can and stick to MEATY bones that are edible.
Feed MEATY bones that are surrounded by and wrapped up in plenty of meat. Do not feed bare bones or bones that have hardly any meat on them. Too much bone can lead to constipation, so feeding very bony parts like beef knuckle bones, chicken wings, and even some rib bones can result in some very hard "concrete-like" poops. If you do feed a bony meal like whole neck bones or a slab of beef ribs, supplement with some raw "meaty meat" on the side to compensate for the high bone content.
If you are still worried, learn the doggie heimelich maneuver and monitor the dog while it eats (which should be done anyway, regardless of what the dog is fed!). And always remember: more dogs die from bloat or from choking on kibble and tennis balls than from choking on raw bones.
As for bones not being nutritious: