Bath & Shower
Shower gel / body wash (most can also be used as liquid hand soap)
Avalon Organics
Aveeno Baby Fragrance-Free Soothing Relief Creamy Wash
Bio-D Fragrance-Free Sanitising Hand Wash
Clinique Deep Comfort Body Wash
Jasön
Shi Kai
Shi Kai is not currently making this, but in the past has had some in stock, in both 12-oz and gallon bottles. You can order the 12-oz on line, and the gallon by contacting them via phone or email. I've found them very responsive.
Whole Foods 365 Fragrance-Free Shower Gel
Shower gel / body wash substitutes
Vegetable glycerin
Available from many stores. Also can be used as lotion and as conditioner. (Do not use as hand soap.)
UK: Boots Value Health Glycerin
http://www.boots.com/en/Boots-Value-Health-Glycerin-B-P-200ml_852418/
Vinegar + conditioner
I usually use 1 tbs white vinegar to 16 oz conditioner. Especially nice for dry skin. This is also a good shampoo substitute. Do not use as hand soap.
Lemon juice + conditioner
I usually use 2.5 tbs lemon juice to 16 oz conditioner. Especially nice for dry skin. This is also a good shampoo substitute. Do not use as hand soap.
Soap (bar and liquid)
Clearly Natural Glycerine Bar Soap -- Unscented
Clearly Natural Liquid Glycerine Soap -- Unscented
http://www.clearlynaturalsoaps.com/cgi-bin/category.cgi?category=LS&item=872577772
(I have not tried this, but I have used the bar soap, and judging from the ingredients list, the liquid soap would also be fine for me.)
Dr. Bronner's Unscented Baby Mild Organic Bar Soap
Dr. Bronner's Unscented Baby Mild Organic Liquid Soap
Dove Pure and Sensitive
US:
http://www.dove.us/Products/Bar-Body-Wash/Beauty-Bar/Dove-Sensitive-Skin-Unscented-Beauty-Bar.aspx
http://www.cvs.com/shop/dove-sensitive-skin-unscented-beauty-bar-4-pack-skuid-972493
UK:
http://www.dove.co.uk/en/Products/Washing-Bathing/Bar/Extra-Sensitive-Beauty-Cream-Bar.aspx
http://www.boots.com/en/Dove-Pure-and-Sensitive-Cream-Bar-x-2_1297931/
Faith in Nature Seaweed Soap ("unfragranced and enriching") (UK)