I was just thinking about this the other day, haha; it was an interesting addition to FR/LG. From Gold/Silver onwards, each game has had its own rematch system (except for Black/White- I can't actually remember if it did :/). This was like the PokeGear only more primitive in that you had to use it in the vicinity of Trainers, which is good because the games were a few years before the PokeGear was invented.
Anyway, I use it in any of the games that have it. It's a great way to grind for experience or money, and also it's fun to see when Trainer's Pokemon level up/evolve when you return to them.