Users typically pursue one of several eligible candidates with the goal of ending up with them, in whatever sense that may be (married, going steady, etc.).
These games are usually in visual-novel format with certain mini-game elements.
If they are allowed to act with free will, or if story progression is enabled, they may pursue a same-sex relationship autonomously.
In The Sims series, every Sim is technically bisexual, as he/she can be directed to have a crush on, fall in love with, engage in romantic interactions and Woo Hoo with a Sim of either gender, provided they are of the appropriate age group(s).
A same-sex relationship is a potential form of relationship in The Sims series.
However, several other Sims are implied to be gay or lesbian in their biographies.
When first played, most Sims either have a completely neutral preference or a slight preference for (or rarely against) one gender.
A Sim's preference scores gradually change as he/she interacts romantically with other Sims during gameplay.
Apparently you can also date your friend/co-worker and also end up getting a 30 minute math lecture, but I was unable to find those particular endings in the game’s decision tree.
Suffice it to say that there are endings where you end up with a wide variety of possible people, but the game is not very satisfying as a dating simulation, since the boring part is what takes so much time and the aspects of dating and romance are brushed over rather quickly.
You set a gender for your character in the presets menu but are allowed to change the body, face and voice actor to fit a different gender.