Unless you are very fortunate, hearing noise from adjacent apartmet dwellers can be a problem.
Here are some suggestions:
1) Purchase higher end wireless headphones that completely cover your ears for tv watching. Don't go cheap! Wireless headphones that utilize the 2Ghz spectrum compared to your local FM radio band is best.
2) Go to your department store and select floor fans that make alot of air rushing noise. Having a constant air rushing sound can go a long way to help cover other sounds plus can be smoothing and help you sleep. Keep them running 24 hours a day so you get accustomed to hearing the fans. You can turn the air flow away from you if needed so you don't get cold. Sometimes you may want to feel the air and other times you just want the air rushng sound.
3) Complain to your apartment manager if you feel neighbors are being unreasonable. Try your best to identify the source of the noise so that your landlord can address it.
4) If you hear noise after 10pm that keeps you awake, call your apartment complex security guard.
5) It may be possible to demonstrate what you are hearing to your neighbor. They may have no idea that you can hear them so well. Keep in mind that if you confront your neighbor in a hostile manner, they will most likely make your life worse! Be polite and maybe even invite them over for a BBQ so you can work the noise topic into the converstaion.
Keep in mind that even if you lived in a single detached family home, dogs barking from your neighbors yard could keep you awake. Noise is all alround us. If you have more than one bedroom, consider changing the purpose of the room if it allows you to distant yourself from noise when you sleep.