In my old image editing program, hitting the delete key would delete the currently selected layer. Apparently not so in GIMP - what's GIMP's shortcut to delete the selected layer?
In the GIMP toolbox, select Edit → Preferences.
Select Interface from the menu on the left, and then click on the "Configure Keyboard Shortcuts" button.
Create a new shortcut for the "Delete Layer" function, I would expand the "Layers" section and click on "Delete Layer".
Type in desired shortcut or accelerator. If the accelerator is already assigned to another function, a pop-up box will give you the option to reassign the accelerator to the new function.
Once you have assigned all of your desired shortcuts, close the "Configure Keyboard Shortcuts" window. Click on the "Save Keyboard Shortcuts Now" button so that you can immediately begin using your shortcuts.
The option to "Save keyboard shortcuts on exit" should also be selected. Close the Preferences window when finished.
You can use Ctrl+X.
This is because standard copy-paste shortcuts can be used to interact with layers. So Ctrl+C will copy, Ctrl+V will paste and Ctrl+X will cut the active layer.
The Del key deletes the content of a selection. If there is no selection, the content of the layer is the selection - so Del deletes the layer's content but preserves the layer itself.