In proper Japanese etiquette, modesty is key. In fact, it's one of the most important aspects.
The proper response to "You are a very great musician", for example, is "Oh no... Not at all!". Any other response is a one-way ticket to social exile. I'm serious. It's necessary to give compliments, but you must take them and keep them private. No one likes a big ego.
This sort of thing is very present in the grammatical structure of formal Japanese linguistics. Often, verbs you use to denote your actions are in the "humble form", whereas when you denote the action of a superior or someone you just met, you use the "Respectable form". You lower yourself and put the other person above you.

After living in Japan for a year, it's something I've grown very accustomed to. So much, that whenever I hear someone brag (not share, but brag) about an accomplishment or make the slightest hint of "I'm better than you are", I feel this overwhelming sense of disgust. In some ways it helps me to keep in line with myself. I tend to keep my accomplishments (and failures, too) pretty well hidden, except for close friends and family. Whenever someone compliments me, I usually respond with "nah not really".
However, in some ways it can be a bad thing. As much as I wish I were back in Japan, I should accept the fact that there are significant differences in what is acceptable here and not. It's still not nice to brag to other people, but it's not a reason to completely dislike a person, either.

It's amazing how a single year changed my perspective this much (and not just on this issue, but many).