In Memento, Natalie and Leonard pass the night together in Natalie's house after Leonard has killed her boyfriend, Jimmy. Natalie is undressing Leonard, uncovering his tattoos and touching his body. In the next shot, we see the two of them together in one bed, Natalie sleeping with her head on Leonard's chest. Leonard is monologuing about his deceased wife. When they part, Natalie gives him a kiss on his lips, stating "I think you will remember me".
In many of the comments that I found, this led people to believe that the two slept with each other during that night. Still, I don't think they did. I see especially Leonard emotionally too much involved with his former wife to engage in it. He meets with a hooker once - without sleeping with her - just to see if he can forget about his wife (he can't). For Natalie there's also no reason (besides a sudden attraction for the killer of her boyfriend). Her goal is to manipulate him, but as Lenny would have forgotten about sleeping with her by morning, it would be a pointless thing to do in this aspect. Also she's wearing the same clothes she did the day before.
I think that Christopher Nolan didn't show how they came to lay together in bed to keep people guessing about it. At least at one point in the movie, he maybe wanted viewers to really not know what happened (being fully in Leonard's position) - so no revelation. Still I think that it doesn't make sense that the two slept together, but I can't be entirely sure. Any indications to support or contradict my impression are welcome.