What to do when you move out:
Leave no furniture behind: You might think leaving a coffee table or a nightstand for the next tenants would be a good, generous thing to do. In some respects it is, but the reality is that the landlord might have to throw it in the garbage anyway as his future tenants might not desire the furniture you've left behind. If you're looking for a recommendation letter from your landlord, don't make him or her do something you should've done in the first place.
Clean, clean, CLEAN: Can you tell that we're stressing this point? Your responsibility is to leave the apartment in the exact same condition it was in when you moved in. You need to do all of the things you typically did to keep your apartment clean while you lived there, but, when you're moving out, you really have to go above and beyond. Remove nails where you hung pictures and spackle the holes closed. Repaint the apartment with the color white, unless otherwise instructed. Scrub the insides of the refrigerator and oven that were provided for you when you moved in. And be sure to fix or replace anything else that was broken by you, i.e. blinds, ceiling fans, etc. For a more extensive, detailed list on how to clean up before you leave, check out this post here. (Some of this info can provide help in how to clean an apartment while you're living in one too...)