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 player character 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 ago. In the Vault Dweller's memoirs it is disclosed that Dogmeat died in the 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 you can locate and recruit 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 descendent 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 health points 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, you cannot give him directions or ask him to leave you. In order to remove Dogmeat from your party you have to get him killed. This can be a difficult task for low level characters. This is because you are unable to talk to Dogmeat and give him orders like you can with normal non-player character followers in the first Fallout.
Dogmeat can be found in the special encounter, Café of Broken Dreams. He can be recruited by the player simply showing his/her Vault 13 suit (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 NCR. If he is dismissed and the player character's NCR reputation is low enough, he might charge at the player character.
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 character's in the game, and this means the player character can command Dogmeat the same as they would command, for example, Sulik.
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.