If there's an emergency condition in your apartment or building, like a major water leak, sewage back-up, or no heat or hot water, you can call 311 to complain to the Emergency Repair Unit. Explain the situation and request an immediate inspection. Don't be shy about calling several times if necessary, to create a record of your complaints and get results. The more tenants in the building who call to report the emergency, the more likely there'll be prompt action. When the landlord does not take action to correct severe problems, City workers may do the repairs and the City will bill the landlord. Whenever conditions are not as they should be and the landlord doesn't repair them quickly, you should speak to a Tenants' lawyer about getting a rent abatement to compensate you for bad conditions and loss of building services.
Attention New York City Tenants: Get information on bad conditions in your apartment at the McAdams Law main site here.