Why do carriers sell the iPhone for so much cheaper than Apple? I've been looking at iPhone 4S prices. I'm not an US citizen but I've been wondering why does it cost only $199 with a Sprint/Verizon/AT&amp;T contract and why does it cost $649 without those contracts?

What are the limitations if I was a US citizen and I was going to use one of those service providers?
In the US, carriers offer phones if you sign up for a 2-year contract at a heavily subsidized price.  The $649 is the price of the phone without that subsidy (retail price).  The subsidy also means these phones are carrier-locked, or bound to one carrier.  You can sometimes get the carrier to unlock these or hack it, but don't count on this.

Citizenship isn't so much a qualifier as having a US credit history and billing address. Presumably the carrier is on the hook to subsidize your hardware so they try hard to ensure you will honor your contract to maintain a stream of payments to them (or they can be fairly certain to collect the early termination fee). Having a US credit card (or cash) as well as having a Social Security or equivalent tracking number so the carriers can run a credit check against their US database of buyers increases your likelihood for being approved for a subsidized phone. If the carriers can't get a good credit check, you may be forced to pay the unlocked prices or buy on the grey market or a used handset.