You can either set the fields to read-only or flatten them. The latter can't be undone, unlike setting to read-only, so it may be preferable. For a convenient method of flattening, you can use the following free JavaScript-based tool: http://www.uvsar.com/projects/acrobat/flattener/
or open the form in Acrobat, open the interactive JavaScript console (Ctrl+J), enter the following line of code:
flattenPages();
and with the cursor on that line, click Ctrl+Enter, or Enter on the numeric keypad. Be sure to save to a new file so you don't overwrite the original since this is not reversible.