Be sure to do your research on the neighborhood and its price of rents when you're looking for your place. These will be good facts and figures to bring in when you're trying to reach a deal with your potential landlord.
You can also do this while you're renting your apartment to see if rental prices around you are going down. If your neighbor is paying less than you, there's no reason why you can't haggle for a lower price to match that as well. Read this sample of letter that a WSJ reporter wrote to her landlord which effectively reduced her rent by $300.