If my apartment building burned down tomorrow, would I be covered?

The building would be covered; your personal property would not. Most landlords would provide temporary housing till the repairs were done but they have no obligation to repay or replace your personal property. Renters insurance is not expensive, you should do an inventory of your possessions in written form or photographs. Keep this record somewhere other than your residence. You can start your insurance for as little as $ 10,000.00 of coverage and increase it as your paycheck allows till you have the coverage you need. One of the things you should ask your agent is about replacement cost on contents. Most insurance policies will pro rate your loss based on the age of the items. Replacement cost on contents normally will cover you up to %400 of the original cost for replacement purpose. This coverage differs between insurance companies and between states that regulate the insurance carrier so ask your agent. When purchasing an insurance policy be sure to read the last page of the policy under the heading exclusions that will tell you everything you’re not covered for.