There are a lot of things in Korean that don't translate to English, but there are plenty of English things that don't make it to Korean either!
1. Bless You!
After someone sneezes you don't have to say anything to them. Rather, you should just ignore it and act like it didn't happen :) It's not rude at all!
2. Sorry for Your Loss
When someone has something bad happen to them, you wouldn't say "I'm sorry" because you didn't do anything! Unless you actually were the person causing their pain, don't apologize! Usually people would say "what do we do?!" to show that they are supportive and looking for ways to make things better. For example: AMERICA - 1: "I lost my wallet!" 2:"Omg I'm sorry, that sucks!" KOREA - 1. "I lost my wallet!" 2:"Omg what should we do!?"
3. No Problem!
In some phrase books they teach you 천만에요 (cheon-man-eh-yo) to mean "no problem!" or "you're welcome" when someone tells you thank you. That's suuuuper unnatural! People just say "아니요!" (ah-ni-yo) which simply means "no" :D