Virginia has several "three strikes" laws, but they relate to particular crimes. For instance, a 3rd offense DUI is a felony, punishable by up to 5 years in the penitentiary. A 3rd offense petit larceny is also a felony, punishable by up to 5 years in he penitentiary. A person convicted of a third violent felony (including murder, mob-related felonies, kidnapping, malicious wounding, robbery, some kinds of arson, and most felony sexual assaults), who has been released from prison or jail between convictions, will be sentenced to life without parole.
Although some three-strike statutes have been held to be unconstitional, many have been upheld by the United States Supreme Court as not being "grossly disproportionate" to the offense, and thus not violating the Eight Amendment's prohibition against cruel and unusual punishment. I do not know what New York state may have decided regarding their laws in light of these decisions.
[This communication is intended as general information and not specific legal advice, and this communication does not create an attorney-client relationship.]