The "free and clear" designation on the label is usually a pretty good indicator. My husband is very sensitive to laundry detergent, so we always buy the "free and clear" kind. It doesn't have to be the most expensive kind, either. Any detergent that doesn't have colors or perfumes in it works for us.
My husband broke out in hives after we used a new laundry detergent, so we've been using the free and clear kind ever since. Most brands have a free and clear version, so it's usually pretty easy to find. The packaging is usually all white, too, so it stands out.