The Company I work For is based in New Jersey. I have a salary of 35,000 annually. They require 40 hrs a week but if we exceed this time we do not get paid for overtime or receive any comp time. Usually overtime is necessary in order to complete dealines. Is this legal?

If you are exempt, your employer does not need to pay you overtime for the additional hours that they may require you to work.

What exactly does it mean to be exempt?

You can read about exemption at: http://www.dol.gov/elaws/esa/flsa/screen75.asp

New Jersey Overtime Pay Law
In New Jersey, work in excess of 40 hours in any workweek must be compensated at one and one-half times the employee's regular hourly rate. In addition to persons working for summer camps, conferences, and retreats operated by a nonprofit or religious association during June through September who are exempt from minimum wage coverage altogether, the following are exempt from the overtime pay standard: (1) executive, administrative and professional employees; (2) employees engaged in labor on a farm; (3) employees of hotels; (4) employees of a common carrier of passengers by motorbus; (5) limousine drivers who work for limousine companies; or (6) employees engaged in the raising or care of livestock. Special rules apply to employees involved in first processing of farm products.

So it sorta depends on how you are classified as an employee.