I can add rows conveniently using Option+Shift+Up Arrow (insert above) or Option+Shift+Down Arrow(insert below).
Is there a keyboard shortcut to delete the current row?
Apple has added the ability to delete a row with a keyboard shortcut. See the attached image.
Delete Rows ALT+CMD+DELETE
With Numbers 11 and earlier, by default, no, there's no shortcut.
You can create one yourself though:
Open System Preferences → Keyboard → Shortcuts → App Shortcuts.
Click the + button to add a new shortcut.
Set the Application to Numbers.app, and the Menu Title to Delete Row.
Set your keyboard shortcut and press Add.
As of at least Numbers 4.3.1, there is a menu item in the Table menu for deleting the current row (as well as one for deleting the current column), with keyboard shortcuts:
Delete Row: Shift+Command+X
Delete Column: Shift+Command+Y
I still had this question (as keycommands are not given in context menu), so the previous answer pointed me to look in the regular menu. In Numbers 12 it is opt+cmd+del/bs