I was just about to post a thread asking about why my desktop icons are keep appearing, but I decided to try one more search in google, and this time I got to what I was looking for straight off.
If you've got an Asus laptop, likely there is an app called Power4Hear Hybrid. That is what is causing desktop icons to keep reappearing when you log in. To stop this, open up the program and click on the Enable/Disable tab, and turn on "Hide Desktop Icons". Then click save and ok. Then the problem will be solved.
I know it's the opposite to a question this is, but it was almost a question, until I suddenly found the solution so thought to just share the solution if anyone else comes across this annoyance.