Every Dragon Age game has romanceable characters, but only a fraction of these romances can lead to marriage. With how busy and dramatic the lives of the companions and protagonists are, only a few of them being open to marriage in the games makes sense. Some marriages can even be done for political reasons, like with Alistair and Anora in Dragon Age: Origins.
Marriage with NPCs are always an endgame event, and NPCs that can marry the player throughout the game series include Alistair, Anora, Sera, and Cullen. However, there are others who hint about being open to marriage or even getting married off-screen, like Sebastian, Cassandra, and Dorian.
Alistair And Anora
Alistair can only be married if the player character is a female Cousland, romances Alistair, gets him to 100 percent approval, makes him King, kills Loghain, proposes to rule by his side as queen, and survives the final battle. This gets the character married to Alistair, and the two rule Ferelden together as a couple. Among the marriages that can happen in Dragon Age, Alistair may be one of the most difficult just because there are a lot of prerequisites.
Anora is a similar story in terms of becoming a ruler at her side, but she is unique in many ways. She is not a companion character, nor does she play a large role in Dragon Age: Origins until the players get to Denerim. To marry her, the player character has to be a male Cousland, needs to support her for the throne, and must propose marriage before the Landsmeet. This is treated as a political marriage, as Anora seems to like it as an "advantageous move." For the marriage to happen, the player also cannot kill Loghain.
Sera And Cullen
While Alistair and Anora have marriages, they happen off-screen, while Sera and Cullen from Dragon Age: Inquisition have marriages on-screen in the Trespasser DLC. Both, of course, have to be romanced, and the player gets a choice whether the characters marry or keep their relationship as is without marriage. In Sera's romance, she proposes to the Inquisitor in Trespasser and the two can get married quickly right then and there, with Sera in a white dress.
Cullen is also the proposer of marriage in his romance. The wedding happens on-screen and takes a little more time than Sera's, with Mother Giselle marrying him and the Inquisitor and vows being read. If the Inquisitor is an elf, they can read elvish vows in the ceremony. In this marriage, it is the Inquisitor that wears the white dress like the one in Sera's marriage.
Hints Of Marriage With Other Characters
While other characters are not said to get married to the player character, there are still mentions of marriage in certain relationships. Cassandra is one such character, as she mistakenly thinks the Inquisitor is going to propose to her in Trespasser if she is romanced. When she finds out she is mistaken, she mentions that she is open to marriage in the future and will act surprised when and if the Inquisitor ever proposes to her. This only happens, though, if she is not Divine. If she is romanced and Divine, she says that they can never marry, though she does love and feel dedicated to the player.
Another NPC that mentions marrying the player character is Sebastian Vael, the DLC character of Dragon Age 2. Whether as a rival or friend, he mentions an interest in marrying Hawke if romanced. If rivaled, he says he wants to marry Hawke as a Prince and that they should be Viscount so that their marriage can make a strong alliance between Kirkwall and Starkhaven. As a friend, he mentions wanting a chaste marriage, with Hawke possibly becoming a sister of the Andrastian faith.
In Trespasser, there is a line of dialogue that romanced Dorian says that has made fans wonder if he and the Inquisitor got married between the events of Inquisition and the DLC. In the Deep Roads section of Trespasser, the Inquisitor can say, "Wandering into peril is practically how we met," and Dorian replies with, "Practically a second honeymoon." This hints that they may have gotten married and already had their first honeymoon.
Dragon Age 4 is in development.