If you do not want the field to ever be visible on that layout, just delete it from the layout. The field will remain in the table and will update as records are modified and a different layout can display that info as needed.
There are also ways to make a field appear and disappear from the layout if that should be necessary.
That is what I thought to do at first - sorry I wasn't more clear. But after I remove it from the layout and then view as table, that field doesn't show. But when I re-add it to the layout, then it shows in table view. I am not sure what I am doing wrong.
It's working perfectly. Recall that I said "if you do not want the field to ever be visible on that layout..."
Since you want to see it in table view, you can leave the field off the layout, but click the modify button in the status area to select it for table view.
Duh. That is exactly what I was needing! Thanks so much!