Leonard Shelby: I have to believe in a world outside my own mind. I have to believe that my actions still have meaning, even if I can't remember them. I have to believe that when my eyes are closed, the world's still there. Do I believe the world's still there? Is it still out there?. Yeah. We all need mirrors to remind ourselves who we are. I'm no different.
Natalie: Is that what your little note says? It must be hard living your life off a couple of scraps of paper. You mix your laundry list with your grocery list you'll end up eating your underwear for breakfast.
Leonard Shelby: Facts, not memories. That's how you investigate. I know, it's what I used to do.
Leonard Shelby: Memory can change the shape of a room; it can change the color of a car. And memories can be distorted. They're just an interpretation, they're not a record, and they're irrelevant if you have the facts.
Teddy: You're not a killer. That's why you're so good at it.
Leonard Shelby: I meet Sammy through work. Insurance. I was an investigator. I'd investigate the claims to see which ones were phony. I had to see through people's bullshit. It was useful experience, 'cause now it's my life.
Leonard Shelby: Now... Where was I?
Leonard Shelby: You know, I can remember so much. The feel of the world... Her. She's gone. And the present is trivia, which I scribble down as fucking notes.
Teddy: So you lie to yourself to be happy. There's nothing wrong with that. We all do it.
Natalie: You sad, sad freak. I can say whatever the fuck I want, and you won't remember. We'll still be best friends. Or maybe even lovers.
Teddy: You know, I've had more rewarding friendships than this one. Although I do get to keep telling the same jokes.
Answer: It is never explicitly given. The most Leonard says on the subject is: "I'd rather be mistaken for a dead guy than a killer." Speculations include (you can make up your own motives as well) : (1) The clothes and car are so much nicer than his. If you are willing to kill someone: stealing is not really a "crime." Why not take the nicer objects? (2) It could be part of his "routine": Kill a man, take his clothes and car. The clothes he had on and the truck may be from the man he killed a year ago. (3) It could be that he wants to make the killer of his wife suffer even more, and takes his clothes as a way of humiliating him. Leonard takes the man's life-his clothes and car, which are wrapped up in his identity-just as the man took his. This idea seems to work with a theme in Memento about "Identity" (especially mistaken identity). Natalie thinks Leonard is Jimmy, then thinks he is Teddy, then learns he is Leonard. Teddy is "mistaken" for the second killer, Jimmy is "mistaken" for the 2nd killer. Sammy's story as a part of Leonard's story, etc. (4) It could "simply" be explained as a "plot device": Leonard has to do it, otherwise he won't find the note in "his pocket" and meet Natalie. (5) Leonard doesn't want to admit he's a murderer. He's lying to himself. If he's the victim, then he cannot be the murderer. (6) Leonard takes Jimmy's clothing as part of his routine of killing J.G.'s he becomes another person, he's the victim not the killer, thus "I'd rather be mistaken for a dead guy than a killer." and that's why he also takes his car, so he has to, once again, find his wife's killer and kill him.