In an experiment with indirect staining, it is very necessary to stain cells with the secondary antibody alone to control for non-specific binding of this polyclonal antibody to dead or sticky cells. This is the so-called "secondary control" that marks the level above which fluorescence intensity can be considered specific. Comparing the intensity of cells stained with the secondary antibody alone to the background autofluorescence of unstained cells is often diagnostic of problems with the secondary reagent. Ideally, the secondary control should be no brighter than the unstained cells.
It is also absolutely necessary to have singly-stained cells to set the spectral cross-talk compensation for multicolor experiments. There is considerable debate, however, about the question of appropriate negative controls when staining cells with a direct protocol. If positive cells are much brighter than unstained (autofluorescent) cells and if the experiment contains some samples where no cells stain, then, arguably, the unstained cells within the stained samples are, in themselves, controls for non-specific staining. Most people, however, feel happier about ruling out problems with dead cells or Fc-receptor binding if their experiment contains samples stained with so-called isotype control antibodies.
Isotype control antibodies are antibodies with no specificity for the cells in question but with all the non-specific characteristics of the antibodies used in the experiment. Since antibodies come in different classes ("isotypes") with different binding characteristics, an experiment should probably have an isotype control antibody for each class of antibody used for staining. Such antibodies are available from manufacturers of flow cytometric reagents.
Sceptics will wonder about our ability to know the protein concentration of every antibody that we are using and to know the number of fluorochrome molecules conjugated to each of these antibodies. Compromises may be necessary, since each stain in a panel of many stains may be of a different isotype, at a different concentration, and with a different F/P ratio -- and will therefore require its own control.
There are no perfect answers here; the requirement for controls is often determined by the nature of the experiment and needs to be considered carefully in relation to the stringency of the questions being asked of the resulting data.
View more details for Control Setting in "Recommendations for Background Control".