I understand your issue and try this if you haven't already...right click your desktop out in open space and select "sort by" and make sure there are NO checks beside any of the options. By default anything new added to your desktop be it downloads, new icons, etc will be placed at the next available slot to the right which is what you are wanting. Also are the downloaded files in the the pic you provided downloaded through a program like a torrent or other filesharing program? If so create a folder where you want it in your documents or on desktop specifically for those downloads and from within the download program select all downloaded files to be stored in that folder, this is normally done by default. IE downloads are saved where you select them to go when you download the files by default.
Check to make sure none of those options are selected and it sounds like the "date modified" one might be selected.
The other thing these other responders are talking about is an icon saver program which is not what you need but search for "desktop icon position saver" should get you to the one I have that works like a charm. I asked about this in the Vista forums related to this site and someone provided a link for the one I am using plus Solway's makes one also. I had to get this because of updating Nvidia vid card drivers
with SLI active rearranges my icons every time I update the drivers.