Yes, MindMyMinistry has a folder system you can organise your songs into.
Creating a new folder
You can create your own folders by using the Song Folders area in the Settings menu (top right on your screen while logged in as an Administrator). Just click the Add Folder link.
You can also rearrange the order your folders are displayed in, rename them, or get rid of the ones you don't use. (Any songs left in a folder you delete will be moved into Unfiled.)