Renter's insurance is a necessity. Your landlord has insurance only on the building. You are responsible for insuring your belongings. Get renter's insurance as soon as you move into your apartment. If you are attending college, however, check to see if your parents' policy will cover you.
Renter's insurance will insure your property within your apartment. Some policies will also cover your property when it's outside of your apartment. For example, if your bike is stolen when it is parked at your friend's apartment, your renter's insurance may reimburse you the cost of your stolen bike. Renter's insurance also covers fire or water damage.
Consider a replacement-cost policy. In the stolen bike example, a replacement-cost policy would foot the bill for you to buy a new bike, similar in quality to the one you lost. Without this, you would receive an amount equal to what your bike is worth minus depreciation, which probably wouldn't be enough to buy a new bike. A replacement-cost policy will increase your premium slightly, but it can be well worth it.
There are limits on reimbursement for expensive items. If you have computer or stereo equipment or costly jewelry, you may want to insure those separately. If you have items of great sentimental value, they obviously can't be replaced and you should put them in a safe deposit box.
Your insurance should also cover personal liability. Most renter's insurance policies will cover all non-auto accidents, including accidents that happen away from your apartment. Let's say that before your bike was stolen, you accidentally hit a pedestrian with it and he or she sued you. You are protected against lawsuits because you have renter's insurance. Although coverage varies, $300,000 is standard coverage for personal liability.
For as much as it covers, renter's insurance is relatively inexpensive. The National Association of Insurance Commissioners estimates that the average policy costs only $169 per year. Compare that with auto and health insurance and it's a bargain.
As soon as you obtain renter's insurance, document your belongings. Make a videotape of everything you own or photos of everything you would want replaced. If you can't do that, write a detailed list of your things. If you lose your belongings in a fire it will be nearly impossible to remember everything you had. A record of your things will be invaluable in settling claims with the insurance company.
Keep your tapes, photos or written list somewhere outside of your apartment - at a friend's residence or with a relative. If you have a fire, you don't want these records destroyed as well.