Dog is one of the main characters introduced in Half-Life 2 and is described by Alyx Vance as being built by her father, Dr. Eli Vance, to protect her after the events at Black Mesa. Alyx has been "adding to him ever since" however and he has grown in size; he's now bigger than any adult human.
Your first meeting with Dog takes place at Black Mesa East when Alyx takes you outside and teaches you how to use the Gravity Gun. The training session plays out as an elaborate game of catch with Dog throwing objects (with his own built-in gravity gun) for you to catch and toss back to him. The game is interrupted however when Scanners fly over and the area is blanketed with Headcrab Canisters. Dog helps you escape to Ravenholm.
He provides further assistance later in the game, during a fight through the streets of City 17 where he uses his intense strength to throw cars at attacking Combine soldiers before finally jumping on the back of a Dropship and being flown away, and nearer the end where he finds a way for you to sneak in to the Combine Citadel.
In Half-Life 2: Episode One dog returns for a brief period at the beginning of the game, digging Gordon out of the rubble. He then acts as an antenna for the videophone. He then later throws Gordon into the Citadel while inside an abandoned van.
In Half-Life 2: Episode Two Dog welcomes Gordon and Alyx at White Forest, and saves them from a strider. Later on, he will also try to kill a Combine Advisor who kills Eli Vance, but he only manages to scare it away, saving Gordon and Alyx.