In what relationship can you skip "san" (sir/miss) in Japanese?

First of all, you would never refer to yourself with the suffix san or chan (unless it was done jokingly). Close friends or relatives you can skip the san as well. Married couples also don't address themselves with the san suffix. Japanese are very averse in using abbreviations, especially for names, so I can understand taka-chan instead of the full name Takako.