Does android store my list of downloaded apps anywhere I can locate them outside of my android device?
Right so after you log in with your phone you sync to the site. Log in to the site and you will see a list of apps installed on your phone.
Me for example I just got rid of my droid for the X. So I just installed Appbrain logged then went to my office and appbrain.com and was able to see the list of all the applications that I had on the old droid. I then copied that checked those apps and selected add to X which was on the drop down menu. Let me know if you need a screen shot.