####### Solução 1 #######
This worked for me win 7 - 64 bit home premium
1) Drive to "Folder Options"
2) Click "View"
3) Scroll down to "Use Sharing Wizard (Recommended)" it must be checked
4) Un-Check the Check -box
5) Click "Apply"......the Icon will be removed from your desktop
6) Re-Check the Check-box .....the icon will not be back
Have fun and try not to mess around with registry
if you do not know exactly what are you doing
####### Solução 2 #######
Hi, I too just had the same issue the the Homegroup icon suddenly appearing on my desktop. I did find a suggestion to right-click the desktop and select "personalise", then select "change desktop icons". The homegroup icon would not be displayed, but it was suggested to unselect "recycle", then "apply" and then reselect. This didn't work (and didn't make any sense anyway). So instead I checked "user's files" and applied. I found that the homegroup icon was replaced by my home folder (which had my name on it). I then repeated the process, but unchecked the "user's files" and applied. Low and behold, the icon disappeared from my desktop completely. I hope this made sense and is useful for others.
####### Solução 3 #######
1) Right-click the Homegroup icon.
2) Select "Create Shortcut" (the shortcut will replace the actual icon).
3) Drag the shortcut to the Recycle Bin.
