I can't really pick between three of them, as I loved them all for different reasons.
I love Knights of the Old Republic primarily due to the memories that I have of it. It was the first game that I had used with the "Duke" controller for the Xbox, which I actually loved the feel of. The story, primarily the twist, still comes into my mind from time to time, the most memorable one for me.
I love Knights of the Old Republic 2 because it introduced me to Obsidian Entertainment. Just because I had seen the logo for Obsidian, I had looked the studio up a few years later, finding out that a large portion of the employees had been apart of Interplay. I had found out that Interplay had created the Fallout universe, so I decided to try those games, which I had begun to love.
And finally, I loved Battlefront because it was the first game that I was able to play with friends and family. I also loved it because no two matches were the same, so I could continue to have many new experiences within the same game.
I don't really know what exactly happened to the original discs that I had for any of the games. I now have the two KotOR games on Steam, but I don't really feel I should get Battlefront 2 on Steam because it has largely been an experience with family on a "large" screen. I guess if I ever see Battlefront 2 anywhere for cheap for Xbox, I'd probably pick it up.