How to delete MS Word table cell contents but not cells

Using the delete key instead of backspace should do it. On a PC, anyway.

If you're on a Mac, and therefore don't have a real delete key (the delete key on the Mac's keyboard is functionally equivalent to a backspace key on a PC), you can do fn + delete to accomplish the desired effect.

The Backspace can be used to delete the highlighted table cells, whereas the Delete key which is usually found in the row above it will clear the contents of the highlighted cells.