There are now many competent free anti-virus and anti-spyware packages. Microsoft's Security Essentials tops the list because of its low resource usage and respectable detection capabilities. For anti-spyware, you have plenty of free options as well, including the venerable Ad-Aware, as well as Spybot Search and Destroy, and HiJack.
This Generally, it's acceptable to install more than one anti-spyware programme, although most experts recommend against installing multiple anti-virus applications.