Without AppleCare+, you'd need to buy a new phone. If you're still under your two-year contract, you're not going to receive the subsidized $200 price. Instead, you'll pay the phone's contract-free price, which for an iPhone 4S is $649!
Apple does occasionally perform out-of-warranty service. Even without AppleCare+, you might be able to buy a refurbished replacement iPhone 4S from Apple for $199 ($149 for older iPhones). But I wouldn't count on that given current demand.