Smoke detectors are vitally important to your safety when living in an apartment. Even if you're extremely safe when it comes to fire, your neighbors might not be. Fire can spread quickly through roofs and other shared areas at the complex, so a smoke detector is often your best bet for protecting yourself.
You should have a smoke alarm in (or at least in the hallway near) every bedroom. The kitchen should have one as well. When you move in, make sure all of your smoke alarms are working properly. Test them out to see if they make noise. It's also not a bad idea to put fresh batteries in them. Be sure and test them every month after moving in, too.
Preferably, the unit should have a carbon monoxide detector installed -- and there should be a working fire extinguisher somewhere in the apartment, too. Don't forget about that!