There seem to be not one but 2 forum threads on this subject. The forum search box is a resource tool that can be used to locate the answers to this and many other questions that have been asked before.
The alphabetical ordering of categories is theme dependent. If you open your categories widget you can use the checkbox to set hyerarchical structure.
You can work around this entire categories issue by not useing the categories widget at all. You do this by creating your own site index page and the instructions for creating a site index page are found in the FAQs blog http://faq.wordpress.com/?s=index+page
Anne, for an exact order, best bet would be to create a Text widget and place the links within it in the order you want it. Even in regular WordPress, that would be the answer since if you need it in a specfic order, there’s really no way that the software can do it currently. Pages can though although themes would be overriding it.