Aha! It works. The instructions and admin page confused me. If you are stuck, here is a detailed explanation of how to get My Link Order to work with WP 3.
1. create Link Categories: On Admin page, Left sidebar, open “Links” menu, select sub-item “Link Categories”, add categories
2. create Links: On Admin page, Left sidebar, open “Links” menu, select sub-item “Links”, add links. Select a category for each as you create it (or edit & select later). Ignore Rating.
3. Install My-Link-Order plugin any time before next step.
4. On Admin page, Left sidebar, open “Links” menu, select subitem “My Link Order”. In center column under “Order Links” you can rearrange the links within each category, one category at a time. Under “Order Categories, you can rearrange the orders in which they will appear in a sidebar.
5. On Admin page, Left sidebar, open “Appearance” subitem “Widgets”. On Right sidebar, open either “Left Sidebar” or “Right Sidebar” as the place you wish to display these links. From Center Column “Widgets”, drag “My Link Order” widget from Center Column to the open Right or Left Sidebar thing you opened in the Right Sidebar.
6. Open the freshly dragged My Link Order widget and set both “Category Order By:” and “Link Order By:” to “My Order”. This applies the order you set in step 4 above.
Forgive the tedious explanation, but it took me hours to figure this out, and I suspect I’m not alone. It works fine, once you get it.