What need do you see in today's society for civil disobedience, how does it fit here today?
Civil disobedience can be applied in any situation where they feel there is a moral compulsion to speak out against perceived injustice. For example, if an individual knows that particular business practice endangers consumers or individuals who are essential in the production of products, civil disobedience could be a course of action. If individuals feel that a particular issue cries out for social attention, civil disobedience might be warranted. Cindy Sheehan, a mother of a soldier killed in Iraq, used civil disobedience to stage protests outside of then- President Bush's ranch in Crawford, Texas. This would be an example of using civil disobedience to raise awareness to a social issue.
This depends, of course, on what country you live in. However, in general, there is a "need" for civil disobedience in any place where there are laws that neglect or infringe on the rights of a group of people. For example, you could argue that civil disobedience is necessary (depending on your politics) to A) protect the unborn from abortion in the USA or B) push for equal rights for gay people (same country).
How civil disobedience "fits in" sort of depends on what you mean by "fit in." In general, civil disobedience will only work to expose a problem that exists but that people are not very aware of. I do not think there are many such problems in the US today.
Civil disobedience is needed in any society, since societies are, by nature, imperfect and always in need of reform. The "civil" part of civil disobedience is important too, in that there is a need for non-violent protest. It is a form of free speech, of constructive criticism of government or business policies, and helps bring about positive change.
In the US, where we have a founding document, the Constitution, civil disobedience is one of the ways in which we cna keep government honest to the original contract. It is a method of protesting what we feel are unjust laws or policies in hopes of making them just policies.