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How have you configured your Categories in Catalog -> Manage Categories?
Two possible causes that spring to mind:
You must have a root category ("Default Category” in this example). The “Default Category” isn’t shown on the front page and is used as a placeholder for the real categories. All your categories should be a sub-category to the root. You can then add further sub-categories if required. In my example I’ve created a test category called “General” as a sub-category to “Default Category”. See the attached “Categories.png” image as an example. On my front page I see “General” (see “Home_page_Demo_Store.png” attached).
If you’ve created your categories all as root categories then this won’t work and will show nothing on your front store. You can drag the categories into your root category so there’s no need to delete and recreate them.
If you’ve got the heirachy of the Categories correct, make sure the categories themselves are Enabled (default = No). Select your category and verify that “Is Active” is set to “Yes” under the “General Information” tab.