There is a rumour that Trend Micro--one of the sites offering free Conficker scans--may have deliberately spread the Conficker warnings.
I have yet to hear of anyone's computer actually getting attacked by this virus.
That doesn't mean it isn't real: http://www.snopes.com/computer/virus/conficker.asp
Just be wary of the anti-spyware you choose. It is not unusual for anti-spyware to actually contain, um, spyware or other malware or adware. Avast!, Zone Alarm, AVG are relatively safe. Norton hogs resources and should be removed, as it is also less effective lately. It comes pre-installed on a lot of new PCs, but it sucks. McAfee is similarly bloated and less effective.