Resignation is an act of maturity in politics and public life. Of course it is a difficult act but not an impossible one. Anyhow, you should know about democracy to do so. And you need some moral and ethical ground to be able to accomplish such a resignation (abdication for monarchs).
There are several cases when such resignations were evoked. The Watergate scandal was fatal for President Nixon, Edward VIII King of England and Ireland for marrying Wallis Simpson, the abdication of Michael I, King of Romania, Dominiques Strauss-Kahn resigned due some allegation around the ELF scandal and some student mutual health insurance from the Cabinet of the socialist PM Lionel Jospin. Horst Koeler, the former German president also resigned. Margot Kassmann, the Chair of the Council of the Evangelical church resigned once he was found guilty for driving under the effect of alcohol. So, as we can see, in some civilized countries is possible to resign and this shows maturity, dignity, morality.
Lately, Germany faced such a resignation of the Defense Minister of Germany, Karl-Theodor zu Guttenberg based on a plagiarism allegation concerning his PhD thesis. He tried to face the allegations first, but finally, once the University of Bayreuth revoked his scientific title, he realized even though he is a good and successful politician, he can not stay longer in this high level position.
Unfortunately, in some other countries like Hungary, Romania, China, Russia, North Korea and lately we have seen horrific pictures from Libya, resignation is not an option. Of course, we can not speak about real democracy in these countries, even though some are EU members. Probably, it is kind of an legacy to do so. I think we still have things to learn. After 45 years of communist dictatorship we just changed some names but even though they pretend to act in the name of the democracy, they are also some guys strongly linked to their positions and they do not even want to know about the term "resignation".
I think we will need again 45 years to learn more about democracy and to act accordingly.