I buy sandwich meat from my grocery store's deli on a regular basis, and while it uses less packaging than buying the pre-sliced kind, I still hate to waste the little zippy bag the meat comes in. After reading about the Rubbish Free Year, I'm really trying to reduce my trash, but I'm not sure it's food safe to reuse a bag that held turkey. My mom came up with a great idea (I'm kicking myself for not thinking of it!).
Take your own reusable containers to the deli! I took two Glad reusable containers (I think they're called "entree sized"), and had them slice my turkey and put it in those instead of a baggy. They have to put a sticker on it, but if you ask them to stick it lightly it should come right off.
If your deli shreds cheese you could buy shredded cheese this way, too.