New York State grants some specific rights to crime victims: 

In New York State all crime victims/survivors have the right to:

Certain kinds of compensation and assistance from the New York State Office of Victims Services
Be notified of judicial proceedings and of the accused’s:
first appearance before a judge;
release from jail while the criminal proceeding is pending;
entry of a guilty plea;
the maximum and minimum terms of imprisonment if the defendant is sentenced to prison.
You may also have the right to be given notice of the release or escape of a person committed to a state mental facility.
Notification of the inmates release and conditions of release
During judicial proceedings
The victims of certain felony offenses shall be consulted by the District Attorney to obtain the views of the victim regarding disposition of the criminal case by dismissal, plea of guilty, or trial.
Victims and witnesses may request assistance from law enforcement agencies in informing employers, creditors, school, or others when needing to miss work, school or other obligations due to cooperating with the prosecution (attending court, depositions, etc).
Be free from intimidation
Submit a victim impact statement
Restitution - Compensation paid to the victim by the perpetrator of a criminal offense for the losses or injuries incurred as a result of the criminal offense.  It is not payment for damages for future losses, mental anguish, or “pain and suffering.”
Other general rights
Get a copy of the police report without charge
Prompt return of property
Waiving payment of fees for replacement of drivers’ license, permit, registration, license plates which are lost, stolen, or destroyed as a result of the crime
Not be subject to discharge or penalty from employment when appearing as a witness in a criminal proceeding
Name changes can be kept out of the public record if the court determines that your safety would be in jeopardy.

Additionally, victims/survivors of Domestic Violence in New York State have the right to:

Go to criminal or family court to obtain an Order of Protection
Have an Order of Protection served without charge by law enforcement officers
If the police find that the abuser has committed a felony they must make an arrest
If they find that a misdemeanor was committed against you they must make an arrest unless you specifically ask them not to make the arrest.  (Even if you do ask them not to arrest, many police agencies will still make the arrest if they have evidence of a crime.)
If the police have reasonable cause to believe that more than one family/household member committed a misdemeanor they are not required to arrest both parties, but must attempt to determine who the primary physical aggressor in the situation is.
Police must arrest when a duly served Order of Protection, or an order that the abuser has direct knowledge of, has been violated by either the abuser failing to “stay away” from you or by committing another offense. 
Have an order of protection honored regardless of where it was issued
Place or temporarily lift a “freeze” on their creditreport free of charge.  Credit reporting agencies are prohibited from sharing with any third party that domestic violence is the basis for the request.
Not be discriminated against by any employer or licensing agency in terms of hiring or employment policies.
Not be compelled to contact your abuser.

Victims/Survivors of Sexual Assault in New York State have the right to:

Be informed by law enforcement in writing of name, address, and phone number of the local rape crisis center
All law enforcement agencies and district attorneys must provide a private setting for interviewing rape/sexual assault victims/survivors
Have a rape crisis counselor, social worker, psychologist, or other professional providing emotional support present during the interview
Not to be asked or required to take a polygraph or psychological stress evaluator exam
Hospitals are required to provide a Sexual Assault Forensic Exam (SAFE),
Hospitals and licensed health care providers are required to accept the state rate for the evidence collection examination.
Victims can choose not to provide private insurance information to pay for the evidence collection examination
Hospitals are required to provide information about emergency contraception (use and efficacy), and to provide it unless the victim refuses or is already pregnant
Hospitals are required to offer victims the opportunity to have a rape crisis advocate present during the exam
Evidence will be collected and kept in a locked separate and secure area for a minimum of 30 days
Request a defendant, at the time of arrest, to be ordered to undergo an HIV test
You are not required to report a sexual assault to the police in order to be eligible for compensation from the state Office of Victim Services