This is how you force Eclipse to use only spaces rather than tabs.  
(Thanks to David Heiniluoma and Cory Kendall)

1) Open eclipse, and go to the preferences section under the Window menu.
2) Navigate to Java > Code Style > Formatter in the navigation tree on
the left-hand side
3) Click "Edit" next to the drop-down menu of profiles
4) Next to "Tab policy" select "Spaces only" from the drop-down menu.
5) You can also change the indentation size on this screen.