I've never, ever used a screen protector ... I'm coming up on my first year as a DS owner (original and Lite, when it came out), and I'm still absolutely scratch free. Smudges pop up, but they're cleanable.
So long as you're not an utter jackass in the way that you play (one of these people that pound buttons as hard as they can when they get excited, as if that'll make your character jump higher or hit harder), you should be absolutely fine. Saying that you "have" to have one is complete bunk. It's nice to have, to be sure, and I've thought about it more than once ... but I have notoriously shaky hands, and it's very hard for me to apply these things without air bubbles.
Frankly, I prefer it without.