I was able to do the same thing when re-signing the lease for my NYC (East Village) apartment in June 2009. My roommates and I drafted a letter requesting a 10% reduction, citing decreased rents 1) in the neighborhood and 2) in the rest of the city - specifically in the financial district where "luxury" buildings were giving away multiple months of free rent as a signing bonus - and the management company accepted it without a word.
Landlords are scared to death of deadbeat tenants like this, it costs a lot of legal fees to get rid of them, and they're freeloading while you're walking through the necessary legal processes.
Every time the apartment goes onto the market they're rolling the dice again - so the value of an existing pleasant tenant is substantial vs. the risk of a tenant of unknown quality.
Which isn't to say you can just get your rent slashed whenever you want, but it's part of the negotiation, and coupled with a recession it can be a powerful argument.
Vast majority of rentals in NYC if you asked the super for a discount in rent you'd be requested not to let the door hit your ass on the way out.
It also depends on the kind of property taxes prevalent in the states. e.g. in California, property taxes are set at the time of purchase, while in Texas they are reassessed every year. So, my landlord (in Texas) basically increases the rent to cover for the increase in property taxes.