The most popular mobile networks in New York are Verizon Wireless, AT&T (formerly Cingular) and T-Mobile. Most students claim that Verizon Wireless has the best reception around the Columbia area, and that T-Mobile has the worst. AT&T and T-Mobile operate via a GSM network, meaning that your mobile phone will be able to roam in most countries (or you can switch to a local SIM card). Verizon uses CDMA technology, which makes roaming a bit trickier outside the US.
The details below pertain mostly to Verizon and AT&T mobile phones since most students ultimately end up using one of these two networks.

Unlike many other countries, in the US you get charged for both outgoing AND incoming calls. The same applies to text messages (SMS) – you are charged even if a text message is sent to you.

CALLING PLANS (current information - subject to change)
Most calling plans involve a flat monthly fee for a specific predetermined number of minutes. A basic calling plan for all networks might cost $39.99 for 450 minutes of incoming and outgoing calls. Usually calls within the same network (e.g. from one AT&T customer to another) are free, and do not count towards your monthly minute quota. Calls made overnight or on weekends are free with Verizon, whereas AT&T provides you with an additional 5,000 minutes of weekend and night calling.
If you use more minutes than your plan allows, each additional minute will cost you dearly – 45 cents.
Unused minutes can be rolled over to the next month on AT&T but not on Verizon.
All networks also provide you with a free or subsidized mobile phone once you sign up for a 1- or 2-year contract. If you already own a mobile phone compatible with the network's mobile technology, you can just buy a calling plan without committing to a contract.

Another calling plan available is Pay As You Go: Instead of paying a flat monthly fee for a predetermined number of minutes, you prepay only for the minutes you want to use. You can add more minutes later as needed. The basic fees are $1 per day of usage and 10 cents per minute. That is, if you use your cell phone on a daily basis, this service will cost you significantly more than a regular calling plan. It is also more difficult and expensive to get data service for your smartphone on a Pay As You Go plan.

All basic plans do not include text messaging (typical fees are 10 cents per message sent/received locally, and 25 cents per message sent/received internationally). Text messaging plans can be purchased separately in addition to the basic voice calling plans (between $5 and $10, depending on the network and the number of text messages sent/received).

Mobile phone companies check the credit history of new customers in order to make sure they can pay their bills. As a newcomer to the US, you haven't yet established a credit history, and you will therefore be asked to pay a deposit, which is returned to you after a year (plus interest). Verizon asks for a deposit of $400, and AT&T asks for $500. You're right, it sucks.
A Pay As You Go plan does not require any deposit.
Attention, Canadians: apparently, some Canadian students have had success using their Canadian credit histories to avoid this deposit. No guarantees, but it doesn't hurt to ask!

1. There is a one-time activation fee of about $25 for Verizon and $35 for AT&T (for a 2-year contract). Activation fees for 1-year contracts are more expensive. The activation fee doesn't apply to Pay As You GO.
2. LOTS of taxes and surcharges apply. If you sign up for the $39.99 plan, expect to pay around $50 per month.

The closest Verizon Wireless store is on 2818 Broadway, at 109th St. The closest AT&T store is on 2540 Broadway and 95th St. (take the 1 train to 96th St.) All companies will also be on campus when school starts.