Intervals allows you to set a project to billable or unbillable when editing or creating a new project. The billable yes/no preference is on the project profile page.
This option controls the default setting for the Add Time dialogue for that specific project. When a project is set to billable, the Billable checkbox on the Add Time dialogue will be checked by default. When set to unbillable, it will be unchecked.
Note: Users can still add unbillable time to a project that is set to billable (and vice versa). When adding time, they will have the option to check/uncheck the checkbox.