If you're a resident of a rental unit, either house or apartment, a sudden problem with the unit can be distressing. If the problem is one that prevents you from using something, you may be inclined to consider it an emergency. However, not all problems are emergencies. Sometimes a serious problem can still be one that isn't going to hurt you and that can sit for a while as the maintenance crew works its way down their list of orders. If you encounter something in the apartment that needs attention, consider these issues before calling for immediate help.
Immediate Threat of Harm
If this is something that would immediately harm you or the structure of the building and make the unit unsafe, call. That's an emergency. A burst pipe is the classic example; the water can do substantial short- and long-term damage to the unit and building, and the flooding can result in both immediate harm and longer-term harm (from mold). The obvious exception is fire — call local emergency services.
Along with immediacy, consider responsibility. Some issues, like gas leaks, are major emergencies, but you would not call the maintenance crew in your apartment for that; you'd call the gas company. If the problem is happening in something that the maintenance crew normally handles, call maintenance. If it's happening in something usually handled by an outside agency, call that agency.
For example, if your refrigerator breaks, that's a maintenance-crew problem. If the electricity in your apartment goes out and causes your refrigerator to stop working, that's generally not a maintenance-crew problem — it's a utility-company problem, and you'd call the utility company to report an outage. If the problem stems from wiring in the building and not a general outage, the utility company will let you know what to do.
Another factor is habitability. If the problem renders the home uninhabitable by reasonable standards, it's an emergency. For example, your only toilet breaks. Even if there are no leaks, if you have no more working toilet, that's a problem. If you're in a unit with two bathrooms, though, and you still have one working toilet, that's not an emergency and it doesn't render the place uninhabitable.
If you have other questions about what might or might not constitute an emergency, contact a property maintenance company. They want everything to go smoothly for you, and they should be able to discuss what they consider an emergency.