An example of intentional, legal disenfranchisement of individuals is how some states in America deny the ability to vote to a convicted felon. This disenfranchisement can range from a matter of several years to life.
Another example is the disenfranchisement of entire groups of people, such as women, various minorities (which minority(ies) varies depending on where in the world you live), or members of some political groups. This can lead to warfare, as in the case of the American Revolutionary War (the cry 'No taxation without representation' conveys this message). This is a good example of the intentional disenfranchisement of a group of people (British colonists in America) by the government in Britain.
A example of unintentional disenfranchisement of a group of people is expounded by supporters of the U.S. Electoral College. Briefly, supporters feel that strict majority vote would disenfranchise the mostly rural American West, by denying them the ability to ever influence an election due to their small numbers. This would be unintentional disenfranchisement as it is an effect of the change, not a direct goal of the change in voting law.