The National Weather Service Forecast Offices serving portions of New England from Taunton, MA, Burlington, VT, Gray, ME, Albany, NY, and New York City, NY all have sites on the Web as does the NE River Forecast Center.
Also well worth visiting by those seeking more information specifically on New England (and the Northeastern US) weather are the Penn State Northeast US Weather Page, the New England Weather Net, the Internet Weather Service, the NorthEast Media of Atmospheric Science NEMAS pages, and John Dietz's Weather Links.
More localized New England weather information can be found at the Mount Washington Observatory, Brad Cummins' Massachusetts Weather Information Page, Matt Douglas' Milton, MA Climate Page, Justin Arnott's Hillsborough County NH Weather Page, Evan Bookbinder's Rhode Island Weather Page, and Derek's Northern Vermont Weather Page.
Many New England TV stations have weather pages on the Web; typically these include the latest local forecast and observations. [A clickable camera icon indicates the station has a live WebCam at their site which may show current weather conditions in the area. A clickable radar icon indicates station has their own local weather radar available on site.]