Bao-Dur:
From The Sith Lords, Bao-Dur is a Zabrek engineer who served in the Mandalorian Wars and the Dark Wars under the Jedi Exile. Before the player meets him, Bao-Dur was a part of a restoration project using his skills to help rebuild Telos IV's surface which had been severely damaged during the Jedi Civil War. When the Telosian government had been ineffective in preventing the Czerka Corporation's depredations Bao-Dur traveled to the planet with hopes of stopping them himself. Overpowered, he joined forces with the player after the Exile had crash landed on Czerka.
When the Exile travels to Malachor V, Bao-Dur uses his remote droid companion to reactivate the weapon known as the Mass Shadow Generator and destroys the planet completely. Bao-Dur is the only one who did not have a clear prediction to his future - discovered to be Force sensitive, but it's later found that he went back to helping rebuild planets damaged by the war.
Master Li:
Master Li, also known as Sun Li, was the Emperor Sun Hai's brother and serves as the father figure to the player in Jade Empire. Before the player's time, Sun Li and his other brother Sun Kin discovered the Water Dragon at the Spirit Monk's temple in Dirge and hoped to recover it in order to end the Long Drought. After taking Dirge and killing anyone who stood in their way, Sun Li and Sun Kin decided to betray their brother - wanting to keep the Water Dragon's power for themselves. The two attempted to kill Sun Hai but he had become too powerful. Li had escaped Dirge but Kin had not and was killed - having his spirit fused into Li's battle armor becoming the terrifying Death's Hand. To make matters worse Li was declared a traitor and Sun Hai ordered his family to executed.
Going into hiding, Li came to the village of Two Rivers and took up a new life as a master at a martial arts school - waiting and planning his vengeance.
Urdnot Wrex:
Wrex is a Krogan from the first Mass Effect and, depending on the player's choices during the first game, appears in a cameo in Mass Effect 2. A bounty hunter and mercenary, Wrex is one of the very few Krogan Battlemasters left in the universe, and as a powerful warrior he comes to respect Shepard's abilities in battle. Wrex also proves to be rather unique because of his interest in Krogan life after the genophage and is planning for a new future for his people.
Near the end of Mass Effect on Virmire the player has the option to either convince Wrex that destroying Saren's work on a cure for the genophage is the right thing to do or to simply kill the enraged Krogan. If the player keeps him alive he then appears on Tuchanka as the leader of Clan Urdnot in the sequel.
Morrigan:
Morrigan is a witch of the wilds and is the second true companion the player comes across in Dragon Age: Origins. Discovered in the Korcari Wilds, Morrigan lives with her mother Flemeth - another witch who supposedly has haunted the woods for centuries. Against her wishes, Morrigan is forced to join the player on his/her quest.
During her time with the player, Morrigan eventually discovers that Flemeth is planning on sacrificing her own daughter in a ritual to lengthen her own life. Upon discovering this, Morrigan asks the player to kill Flemeth. If the player refuses she will leave right then and there but comes back at the time of the Final Battle.
At the close of the game when the player discovers that a Grey Warden must die in order to slay the Archdemon, Morrigan presents the idea to conceive a child with her. Through a ritual the Archdemon would become trapped within the child - allowing the player to live. If the player chooses to follow through with this the ritual will go through and a pregnant Morrigan will flee into the unknown never to be seen again.
Morrigan is one of the two female love interests for a male player and is supposedly one of the toughest to appease (although one of the easiest to lay). She disapproves of the player helping people without gain and particularly dislikes Alistair and the other "good" characters.