There is little difference between the ethics of an online or web-based course and those of a traditional face-to-face course. Cheating is cheating. In an online course, the temptation may be greater considering the fact that a student may never meet the teacher.
Also, a student may forget that the words they see in an electronic discussion belong to another student (or even the teacher), and are thus deserving of the same respect and confidentiality. If you have personal business to discuss, a packed classroom would not be an appropriate place. The same goes with online course message boards- don't post anything you don't want everyone to be able to read.
There are a number of resources available online for more information.