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Avast! specializes in viruses, so although it may block some spyware, it is a good idea to have one or more anti-spyware programs. You will find some good information and links for free anti-spyware programs in this thread:
http://forum.avast.com/index.php?topic=26342.0
Which anti-spyware programs will work best for you depends on a number of things–your OS, other programs, surfing habits, etc.
And a good firewall is essential.
I hope this helps. Welcome to the forums!