What are some supermarket brand soaps and shampoos that are vegan?!

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Dr. Bronner. They sell it at Target.

Oh babe, you are not going to find that stuff - the real stuff with integrity, at any of the stores that you mentioned. Go to your natural food store - look on the Peta2 site for product recommendations and steer clear of anything unless it has the leaping bunny label or it says "Cruelty Free, and Vegan". I would try Vegan Essentials.com online - they have the best stuff and they have a 15% off your order sale going on today - (Friday 12/17/2010).
Offhand, I would definietly recommend Jason, and Nature's Gate.ShiKai is pretty good, too. I also recommend Dr. Bronner's for soap. The liquid soap last for a long time, and is really good.
Even if a product says it doesn't test on animals, doesn't mean that they somehow don't endorse it on individual ingredients. Sometimes the source of one or more of their ingredients tests on animals. And even if they don't test on animals, it doesn't mean that they are also vegan - and have absolutely no animal products.
Consult some animal rights and vegan sites or just go to veganessentials.com and go from there. There are a couple of other online vegan stores, but I recommend Vegan Essentials - they are the best.

A Vegan.

Redwin Sorbolene Bodywash will cover you for the body and even the hair. It is just sorbolene made from minerals so provided you rinse it off it may be okay. The question as to whether it has been tested on animals, which is of concern to some vegans, I am sorry I can't answer.
Innika, Lush, Sukin, Natural Instincts, Arbonne, Mary Kay and Melrose hemp milk are said to be cruelty free brands.

http://www.thebeautyreview.com.au/2007/J…
http://vegesorb.com.au/Vegesorb-Versus-S…
http://health.org.au/

Almost all of those stores have a "naturals" section in beauty supplies... check there, and check labels! :)

I've found some amazing products at Walgreens of all places... Out of Africa and Burts Bees have been my favorite brands (however, if you do not use honey, you should probably find a different brand than Burts). Check ingredients, and check for a "we do not test on animals" labeling on any of the products you see in this section at your local store(s).

These guys are good: http://www.jason-natural.com/
it's all 'leaping bunny' approved too which means that theres no animal ingredients, and no animal testing in any stage of production. it's not that cheap but i find that their stuff tends to last a while, and makes ya smell pretty nice too!

Vegan

Dr Bonners is excellent stuff as someone suggested.
To find more use the link to Petas website with products. If you look on the right side you will see a section that lets you choose things you want about that company. It has a bunny in the block where the search is and is titled SEARCH FOR CRUELTY-FREE COMPANIES AND PRODUCTS

http://www.peta.org/living/beauty-and-pe…

Mm, I don't think you'll find anything cheap. Oh, and keep in mind you can order off of Amazon. Look on there. I use Pureology, but it's $25 a bottle. Just to warn you. There're cheaper things though.

My fav is natureclean
http://www.naturecleanliving.com/