Marriage
A Sim can propose to another depending on their relationship. If the other Sim accepts they will get married.
The Sims
In The Sims, anyone can get married. Either Sim can propose, but the proposer must be at home to do it. Whether the other Sim accepts or not depends on their mood or the relationship between the two Sims. If the other Sim accepts, however, both Sims will change into their formal clothes and share a dance together, and the proposing Sim will be charged §1000. Sims who don't have §1000 can still marry; they'll be charged half of whatever funds they have. The Sim who was proposed to will take on the family name of the other Sim and move in with them. Since there are no defined family ties or family relationships in The Sims, the option to get married is not available to Sims who already live together. Players can stage marriage ceremonies between Sims who live together, but the 'Propose... Marriage' interaction won't be available because they're already considered part of the same family.
Same-sex couples (or two friends of the same sex) can ask one another to 'Move In' if they do not already live together. Whether the other Sim accepts depends on their mood, their relationship, and the quality of the other Sim's house. The Sim who moves in will take on the family name of the Sim who proposed, even if the two are simply good friends. (This is unavoidable, as Sims in The Sims do not, properly speaking, have surnames.)
Marriage in The Sims is an event, not a condition. So, while Sims cannot get a divorce, a Sim who has married into one family can marry out of it, and into another family. Also, if the relationship between two Sims in a family is low enough, they can choose the Attack option and fight each other. Which Sim wins depends on their Body skill. The Sim who loses may choose to move out, and if they do, they will never be seen in the game again.
The Sims 2
When two Sims are in love they can get first engaged and then marry (with or without a wedding party). If the Sim to be married is not living with his or her partner yet they will move in as soon as the wedding ceremony is over. Either Sim can propose.
The Sim who initiates the 'Get Married' interaction is the Sim whose last name both parties to the marriage will take. However, a program such as SimPE can edit this.
There are two ways in which Sims can get married. Engaged Sims can get married with the "Get Married" interaction, in which the two Sims exchange vows and kiss to signify their marriage. It also possible for two Sims to get married under a wedding arch without throwing a wedding party.
The other way, and more "traditional" way to get married is to have a wedding party. This is basically like a normal party, only the Sims are expected to get married. The wedding arch may or may not be used. But a difference between normal parties and wedding parties is that any guest invited will show up even if they have a low relationship with that Sim!
Joined Union
Marriages between two Sims of the same sex are referred to as "Joined Union" in The Sims 2, although a Wedding Party is still called a wedding party. A Joined Union is the alternative to a marriage available for same-sex couples.
Like a regular wedding, when two Sims of the same gender are in love they can get first engaged and then enter a union (with or without a wedding party). If the Sim to be joined is not living with his or her partner yet they will move in as soon as the wedding ceremony is over. Again, the Sim who initiates the interaction is the one whose last name both parties to the union will take.
Sim unions provide fewer aspiration points than marriage. However, a hack available at www.simbology.com allows same sex partners to enter marriages with the same titles, wants and fears as with opposite sex partners. Same Sex Mods
The Sims 3
Sims who are in love can propose marriage and become engaged. They can then either have a "Private Wedding" or a wedding party.
When they wed the last name taken by the couple will be that of the Sim who did the proposing. If the Sim whose name changed had children from a prior relationship, the children will also take on the last name of their step-parent. It is important to note that a Sim's last name can be changed via an interaction performed by the Sim in question at the City Hall.
If the player wishes for a Sim couple to get married, the player first must build up their relationship until they are in love, and have a romantic interest. Then after they have a full relationship bar, the action "Propose Going Steady", under the romantic section, will become available. Sims will then become boyfriend and girlfriend. When they have a full relationship bar once more, the player can have one Sim propose marriage to the other. Unlike in The Sims 2, where same-sex partners were only allowed to have civil unions, in The Sims 3 they can have a marriage the same as opposite sex partners.
It is also possible for a Sim to get married to a ghost or to a Sim who has become a mummy in The Sims 3.
Sims in The Sims 3 prior to a recent patch could also use cheats to keep the Grim Reaper on the lot after he has taken a Sim's life and marry him. However, this would cause that particular Grim Reaper to be replaced by another and lose the ability to collect Sims' souls.
Throwing a wedding party
In The Sims, if a Sim accepts a proposal, both Sims will change into their formal clothes and share a dance together, and the proposing Sim will be charged §1000. Of course, players can arrange for this to happen as part of a wedding party if they so choose.
In The Sims 2 and The Sims 3 a wedding party can be held by selecting "Throw Wedding Party" on the phone. This is basically like a normal party, only the Sims are expected to get married. The wedding arch may or may not be used.
Like normal parties, a wedding party is rated by how good it is. So, it is possible to have a horrible wedding party. In order to prevent this, set up the wedding party like a normal party (having music, buffet table, bar, etc.)
Finally, when the marriage takes place, both Sims switch into wedding attire (which is their "formal" wear, so make sure to choose something wedding appropriate beforehand) and head beneath the wedding arch. Your guests gather around, and the Sims exchange vows and kiss to signify their marriage.
Interestingly, in The Sims 2, if the wedding party takes place with many family members around, and there is music playing, the bride may experience a want to dance with her father after the ceremony and the "first dance" with her husband.
If the "Wedding Party" is successful a limo will come for the couple to take them on their honeymoon. While they are on their honeymoon, the newly-wedded Sims' need bars will have a significant increase. If Bon Voyage is installed, the player can arrange for the Sims to have an actual honeymoon trip.
Divorce
Contrary to popular belief, it is possible for marriages in the Sims' world to end in ways other than death in The Sims 2.
If two married Sims have their relationship with each other fall enough, such as through witnessing an affair, one Sim can kick the other to the curb. To have the couple get a divorce, choose whichever Sim will do the breaking up, click the other spouse, and select "Break Up". This option will only appear if the active Sim's relationship is low enough with their spouse. The divorcee will then flee the lot and reappear in the Family bin in the neighborhood screen. They have no chance to take any children they had or remain in the house. If the player wants them to stay in the house living with their family after the divorce, they will have to be moved back in.
Avoiding Divorce
To avoid divorce wait for their fury with each other to subside or, in The Sims 2: Apartment Life, have them perform the interaction called "Repair Relationship With..." which will have the two Sims attempt to deal with their marital problems.