In The Sims 3, it is rumored that having a same-sex couple in the active household will increase the chances of other Sims in the neighborhood's inactive households autonomously forming same-sex relationships.
However, occasional same-sex relationships do develop autonomously regardless of whether the active household has one, though they are not so prevalent.
In The Sims, same-sex couples can move in together, but cannot marry.
However, marriage is not a recognized state in the game, only a brief social interaction, and no formal relationships exist between Sims.
Therefore, once the "Marriage" or "Move In" interaction is completed, the game no longer distinguishes between gay or straight couples.