Xor,

That term "data validation" set me on the right course. I was able to remove several "input prompts" at the same time by doing this:

1. Select cells that have input prompts that you want to remove.
2. Select the Data tab.
3. Find the Data Tools section of the Data menu ribbon and click on the down arrow next to Data Validation.
4. Select Data Validation. You may get a message that says "The section contains more than one type of validation. Erase current settings and continue?"
5. Click OK and you will get a Data Validation dialog box.
6. Uncheck "Show input message when cell is selected."
7. Click OK and voilá! No more input messages!

Thanks for the lead, Xor!