In the VeggieTales version of the story of Esther, Vashti, the queen of Persia, was divorced by her husband, the king, because she refused to make him a sandwich. I assumed, by the ridiculous and anachronistic nature of the situation, that the actual story was rather more serious, and perhaps more "adult," than the VeggieTales version. That, or it was left completely unexplained, forcing the VeggieTales writers to invent an explanation.
As it turns out, I was right the first time. In Esther 1, we read that Ahasuerus, king of Persia and Media, was holding a feast, and he commanded his chamberlains "to bring Vashti the queen before the king with the crown royal, to shew the people and the princes her beauty: for she was fair to look on" (Esther 1:11). Essentially, he wanted to show her off. Naturally, she refused to be objectified in such a manner, and for that, she was replaced as queen.
Part of the reason Ahasuerus put her away was that the princes warned him that she was setting a dangerous precedent:
For this deed of the queen shall come abroad unto all women, so that they shall despise their husbands in their eyes, when it shall be reported, The king Ahasuerus commanded Vashti the queen to be brought in before him, but she came not.
Likewise shall the ladies of Persia and Media say this day unto all the king’s princes, which have heard of the deed of the queen. Thus shall there arise too much contempt and wrath. Esther 1:17-18
The "contempt and wrath" that the princes feared was that their wives would no longer obey their whims. And, granted, legitimate legal authorities should be granted a certain amount of obedience and respect, in that their just laws should be obeyed. But in the context of wives and husbands, Vashti did nothing wrong.
Wives should not be subject to the orders of their husbands. If husbands are to rule in their households, they must rule as all rulers should: fairly, justly, and with the consent of the governed. Granted, any sufficiently large group must have some form of government. Someone has to be "in charge." But the individual members of those groups should, at least in most cases, retain the freedom to "opt out" of group activities, especially those that are arguably sexual in nature, such as being presented for others to ogle at. It was not wrong for Vashti to refuse her husband's order. It is not inherently wrong for any woman to refuse her husband's demands.
People do not own each other. No one person is or ought to be any other person's slave. Nobody has or should have absolute authority over anybody else. It was absolutely within Vashti's right to disobey her husband's command, be he king or not. Granted, it was also likely within Ahasuerus's right to have a no-fault divorce, since a marriage, while a commitment, must remain a mutually voluntary one. Ahasuerus likely had as much of a moral right to divorce Vashti as Vashti had had to disobey Ahasuerus. Of course, that's not to say that she gave him any valid reason to divorce her. In my opinion, she did not.
I will admit to not being fully familiar with the situation. There are likely dozens of important details that I don't know. But from what I've read, in my modern opinion, Vashti did absolutely nothing wrong.