Most commonly seen as feral beasts that plague the wastes and kill livestock, they are necessary for many struggling wastelanders. There is also the rare cases of domestic breeds that act as companions towards their human counterparts.
Humans are the only species known to truly tame and domesticate these canines. Although other types of sub/meta-humans show an interest in doing the same, dogs of all types, including feral dogs, are well-known to attack or flee from them on sight.
Through the 200 years since the Great War, dogs have remained relatively unaltered by radiation. Other than that, there is no reason to believe that the biology of dogs in the Fallout universe differs from dogs in the real world, besides having a rougher appearance than domesticated dogs, unsurprising in the harshness of the wasteland.
Kyle - Abandoned dog at the Neponset Park overpass.
Junkyard dog - Possible purchase via a random encounter with the dogs owner/ breeder, Gene. The junkyard dog is not a companion but rather assigned (like a settler) to any Settlement. When the dog arrives the designated settlement receives 5 Defense rating buff. (Looks vary at random from Rottweiler to mutt) and as a level 1, has 180 Hit Points so most likely actively defends the settlement also. (This is repeatable and will have a new dog to sell on each encounter)
Finding armor on killed attack dogs, normally found accompanying raiders, will allow one to equip it on Dogmeat. However, no resistance is gained by equipping them.
Vault-Tec Workshop Dogs can be caught for a settlement using dog cages included as part of Wasteland Workshop. Caught dogs will increase a settlement's happiness and defense levels. Mongrels, on the other hand, will decrease happiness and increase defense.
Creation Club There are 12 additional (non-follower) dogs available for purchase from Creation Club: Black Labrador, Chocolate Labrador, Yellow Labrador, Shiba Inu, Rottweiler, Pitbull, Husky, Great Dane, Golden Retriever, Dalmatian, Boxer and Border Collie.
Creation Club There is also a device that can be bought from the Creation Club called a 'transDOGrifier' which gives four new coat options for Dogmeat as well as letting one change his breed to any of the above that have been purchased.