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I usually find the movies with the most replay value, are the ones that transport me to a world I'd be happy living in. The characters become like old friends, you study the subtle nuances in their dialogue, the little ticks, the way they walk.
The 1980 Robert Zemeckis comedy Used Cars is a film I've seen more than any other. There's a particular scene in that film I could watch over and over, it's the bar scene at the end of Rudy (Kurt Russell) and Barbara's (Deborah Harmon) first date. She announces she's going to be leaving town, and Russell gives her a sob story saying it's 'the most fun I've had with a girl...ever' before looking down glumly at the bar. She of course falls for this and turns to head back to him. On seeing that she's taken the bait, Russell quickly licks his lips with a look of mischievous glee on his face. It's a tiny detail in the film that to alot of people would seem completely insignificant. But after repeated viewings it becomes your payoff, you anticipate it, you smile, it's your own personal special moment, then it's gone until the next time.
I also often find myself looking past the characters at the background detail. A picture on a calender, an extra walking by, a shop window advertisement etc etc. It serves to add depth to the fantasy, you're comfortable there, you want to know the place inside out like your own front room.