Dogmeat is a dog that can be found in Junktown in 2161. He can be found terrorizing Phil, an old man in Junktown, by remaining at the doorway to his house and keeping him out. The Vault Dweller can distract him for the old man and, by doing this, recruit him as a companion.
His previous owner had been killed by thugs hired by Gizmo (most likely the Skulz) about a month before meeting the Vault Dweller. In the Vault Dweller's memoirs it is disclosed that Dogmeat died in the Mariposa Military Base after running into a force field (although in the game, it is possible to survive the military base with Dogmeat alive - usually by sealing him inside different rooms to protect him from the super mutants).
Dogmeat is also a special non-player character who can be located and recruited in Fallout 2. He can be found in the special encounter "The Café of Broken Dreams", though this is an easter egg and should not be considered canon. However, a descendant of Dogmeat is found 116 years later in the Capital Wasteland, so it is possible that the Fallout 2 iteration is also a descendant of the original.
He is incredibly effective in combat, as he can do three medium to high damage attacks per turn, and has the same number of HP as a full-grown man. However, one should think carefully before getting him to follow them. He will become a follower, but will not behave like other non-player characters in Fallout, he cannot be given directions or asked to leave/wait. In order to disband Dogmeat he has to die. This can be a difficult task for low-level characters, because it is impossible to talk to Dogmeat and give him orders like with normal companions in the first Fallout.
Dogmeat can be found in the special encounter, Café of Broken Dreams. He can be recruited by the Chosen One, by simply showing their Vault 13 jumpsuit (in other words, undress) and speaking to the dog. Dogmeat will remember the Vault Dweller from Fallout and join the PC. When not in the player character's party, Dogmeat fights for the NCR. If he is dismissed and the player character's NCR reputation is low enough, he might charge at them.
Dogmeat was made even more powerful than his past version. It is not uncommon to see Dogmeat move obscene distances and attack five to six times during his turn. He was also given normal scripting commands like the other non-player characters in the game, and this means the player character can command Dogmeat the same as they would command, for example, Sulik.
Dogmeat can be obtained as a follower in both games regardless of the player character's Karma.
Unlike humanoid non-player characters, Dogmeat cannot wear armor, equip weapons, or use items, although he can be administered stimpaks by the player character and has a Damage Resistance & Damage Threshold equal to that of leather armor.
Dogmeat is a reference to Mad Max 2 (aka The Road Warrior) and A Boy and His Dog. Both movies featured a lone wanderer and his dog-companion in a post-apocalyptic world, and in the latter movie, the main character uses "Dogmeat" as a disparaging nickname for his companion.
Phil confirms the point above when he describes Dogmeat's former owner in the original Fallout: "Oh, the guy was tall, dark-haired with a little graying around the edges. He was dressed all in black leather, like that's a good idea in the desert, and carried a shotgun." The description matches all of Max's characteristics in Mad Max 2.
Scott Bennie was the designer who came up with the name "Dogmeat" for the in-game character. The name was initially applied to Jake's dog in the Hub (previously called Dogshit). Later, it was applied to the current non-player character Dogmeat, either by Tim Cain or Jason Anderson.
The namesake for "Dogmeat" is Vic's canine companion, "Blood" (also called "Dogmeat" by Vic) in the movie "A Boy and His Dog" (1975) starring Don Johnson and based on the novel by the famed sci-fi author Harlan Ellison. This movie dealt with post-nuclear war survival with "Dogmeat" apparently conversing with Vic as they both scour the wasteland for food and women.