Does avast check for spyware? If not, is there any free spyware checkers?
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!
Thanks a lot! 
You’re welcome.
BTW, although I use Spybot Search & Destroy, I do not use the “Tea Timer” part of the program–I found it to be more bothersome than it was worth.