Which free anti-virus/spyware can remove threats detected during on-demand scans? 

It is important to remember that most antivirus software does not have antispyware built in and antispyware software usually does not have antivirus abilities built in. I cuurently recommend AVG for antivirus and I like AdAware for antispyware.

Now if your antivirus software cannot remove a virus then the reason is because it is usually a complicated process or the virus mutates when it tries to delete it (ie makes copies of itself). The antivirus maker usually has the instructions on there site for removing the virus so I would take the name of the virus and search their site or use one of the search engins.