My favorite random sim story was this. I created a cute young adult female, and moved her in to Lucky Palms. After moving to town she decided to become a police officer, and her partner was Donnovan Steel. Here is a picture of him from the Sim Wiki site.
http://vignette1.wikia.nocookie.net/sims/images/a/a8/DonnovanSteel.png/revision/latest/scale-to-width-down/250?cb=20130623215527
Anyways the two ended up becoming romantically involved, and she eventually became his girlfriend. The one evening he called her up and asked if she wanted to come over for a visit, which she gladly accepted. When she came over, he was in the process of making dinner, which she accepted this as well. Things got a little cozy, and they ended up falling asleep in his bed. Around 3 am he got up and informed her that she needed to go home. I had forgotten to have her to ask him if she could spend the night. Anyways, because of this she was getting ready to walk out the door, when he stopped her, and asked her to move in with him.
My second favorite random sim story was another involving Matthew Hamming from Bridgeport. In case you don't know who he is, he is at the top of his profession as a movie star. Anyways, Matthew has the commitment issues trait. The sim I was playing was involved with him romantically, and he ended up getting her pregnant. This particular sim was very very poor, and could barely afford food, much less to buy things needed for a baby. As soon as Mathew learned that she was pregnant with his baby, he asked her to move in with him.
And my third favorite story was involving another young adult female, who got romantically involved with Vladimir Schlick. He is a vampire from Bridgeport (and one of my favorite premade sims). With him, I wasn't planning on doing anything past a bit of romantic interactions, which ended up getting her pregnant with triplets. I'll give you a heads up, this was not the only time I had him produce triplets. Anyways, this woman too was poor a well, not as poor as the other woman I mentioned earlier, but poor. It was a bit of a shock when I saw her come out of the hospital with three babies. Very shortly after this had happend, all of a sudden the game had given this poor woman 42,000 semolians. I'd like to think it was Vladimir, doing the right thing in providing for his babies. Anyways, this couple did end up getting marrried later, and they had another 3 children.