I absolutely can recommend
a-squared Free which is a freeware tool to scan for spyware, adware, worms and other malware. Of course there still is the classic
Spybot Search & Destroy which works just as well. AdAware may have been great in the past but has long since been overshadowed by better alternatives.
An anti virus software is another thing altogether. There does exist free software as well but I have no experience with them. You either want to use something from Symantec/Norton or McAfee, because both are very easy to use and allow a satisfactory protection of your computer.
Keep in mind that most so-called anti-virus software with additional adware/spyware features will never be the way to go, because dedicated scanners like a-squared or Spybot S&D are the best in their job.
