You can add a "bluing" agent to your laundry. Borax is also good for brightening whites. Stay away from chlorine bleach, it can yellow your whites.
Hydrogen peroxide will whiten and brighten clothes, disinfect laundry, and remove stains. Pour it directly on stains such as blood. Since most commercial oxygen-based bleaches are composed of ingredients that break down into hydrogen peroxide along with some brightening additives, you can use three-percent hydrogen peroxide instead. Simply add one cup of hydrogen peroxide to the washer drum before adding water or clothes
oxygenated bleach, not chlorine bleach works. Trade name = Oxyclean
I agree with Cheryl that oxyclean works well. What kind of fabric is it that you're trying to whiten? I know that some people put old linens outside to bleach in the sun as well.