Antispyware soft

Hello,
I got the pop ups stopped, but the icon fot this stuff still comes up when I turn my computer on. It hasn't given me any problems. I right click the icon and a tag comes up "remove soft ware safly. Onc\e I click the tag a pop up box comes up. I go through the procedure and the icon disapears. How do I get rid of the icon, and is the virus going to come back.