Sorry to hear about your situation. My last apartment was a large studio; in fact, it had been a large hall that was ultimately divided into two mirror-image studios. The wall between the two apts was somewhat thin, however, it didn't quite form a seal where it met the ceiling (ceilings were approx 15'). Long story short, I could hear every bleeding thing that went on next door. To make matters worse, my neighbor had a bad singing habit and was ALWAYS home. Furthermore, the guy below me worked third shift and would sometimes watch movies directly below my bed while I was trying to sleep; subwoofer shook my bed...earplugs can't block that out. In the first case, it took a letter from the landlord to shut the singer up. In the second case, some civil words and agreed upon times to make noise solved the problem.
As far as the stomping goes, your neighbors are douchebags. Apartment living is a two-way street. If you live below someone, no loud music or tv during late hours. If you live above someone, remove your shoes and tread lightly, put felt pads under chair legs, etc... In both cases, people need to respect the right of others to coexist. In other words, be as patient and zen as possible about reasonable amounts of noise, while at the same time, making as little noise as possible. Good luck; apartment living can be really nice!
Edit: Damn! Just bumped a really old thread w/o realizing!