Not all noisy neighbor sounds come straight through the walls. This writer once had a neighbor across the hallway blare jazz music at all hours of the night. On some nights it was the perfect mood music, other nights it was just plain annoying. If you have too much noise coming from the hallway you can help reduce it in several ways.
The first is neoprene seals that go around doorjambs edges. Even a small opening around a door can allow a lot of sound to pass through. So add these acoustic seals around your doors if your neighbor makes a lot noise from across the hall. If you're landlord doesn't mind you adding a few modifications to the door, you can also install a door bottom that drops a neoprene shield between the outside of the apartment and the inside to add an extra layer of sound protection.
If sound is coming from your ceiling, there's probably not a lot you can do unless you own the space and can make sound-absorbent modifications to the ceiling, like adding a drop-ceiling or coating the ceiling in Green Glue. But if the noise is coming from below adding some heavy rugs will absorb some of the sound. Even if you have carpets already, adding more density with some extra rugs will be better than just leaving the existing carpets to do all the work.