I thought I would make a list of some stuff that worked for me. All of them have no petroleum products. Keep in mind, what works on one person might not work on another (hence one of the reasons they can't just give a cure-all).
Alba Botanica Unscented Original Body Lotion. This worked very well, I just wanted to try something else after a while.
Avalon Organics Peppermint Hand and Body Lotion. Yes, it has scent, but I have found (through experimentation) that natural scents from essential oils do not cause me problems. Please test before you use! The last thing you want to do is cause an attack all over. Do a spot treatment, and see your reaction.
Almond Oil. Just plain almond oil. When my eczema's not acting up, and I don't need much moisture, I use this.
Jason Natural Aloe Vera Satin Soap for Face and Hands. I have also used their Tea Tree version. I only use this as a hand soap. It contains Sodium Myreth Sulfate (not Lauryl/Laureth). Some people react to that one still, but I'm usually fine, as long as I make sure I get all the residue off, and moisturize afterwards. They also have a body version, which I like for bubblebaths.
Dial Complete. Because it's prefoaming, it leaves less of a residue on my hands. I use this when my hands are really dirty, though. Does contain parabens.
As I stated before, this is just what I have seen works for me. I still get flair ups, but they are far fewer than they used to be. Also, if you have the time and patience, I highly suggest making your own products at home. I make my own exfoliators, to make sure I'm not allergic/going to react to anything. A good book for how to make your own products is Earthly Bodies & Heavenly Hair by Dina Folconi. While I do not aggree with all the stuff in that book (my face plus oil is not a good combination), the directions to making your own products are excellent, and it also gives suggestions for preservation and shelf life.
Hopefully this will help some of you. As always, do a spot test before you cover the entire area, and check ingredients for things you might react to.