I have a worksheet in which Excel does not allow me to change the
alignment of a range of cells from, say, left-justified to centered.

I am experienced with Excel/VBA and have not seen this before.  The
cells are not protected and do contain numerical data.  If I add a
leading apostrophe to the cell values to have them treated as strings,
I can then align the cells however I like.  When those cells contain
numerical data, Excel will not allow me to change the alignment from
left-justified, regardless of whether I use a toolbar, the Format tab,
or VBA.

Any ideas?