Here's a good article on two vs. three prong devices:
http://electronics.howstuffworks.com/question110.htm
Take note of the last paragraph "What happens if you cut off the ground prong or use a cheater plug so you can plug a three-prong appliance into a two-prong outlet? Nothing really -- the appliance will still operate. What you have done, however, is disable an important safety feature that protects you from electric shock if a wire comes loose."
I suggest you be very very careful with electric appliances in your apartment.