In my home, we use Cheer Laundry Detergent. After being married to a man with uber-sensitive skin, and then passing that trait to our children, we have found that Cheer will not irritate or aggravate any of their skin conditions. All of our clothing comes out clean, soft, and smelling great.
I use the liquid, because it dissolves into the wash easier, and doesn't leave any residue on the inside barrel of the washing machine.
We use the Cheer for dark clothes on our jeans and similar items; it keeps the colors from fading out, and the clothes look newer longer.
I've tried other detergents, and while some others also will not irritate the family's skin, they don't get the laundry as soft and clean as Cheer does.