Yes, basically it will keep coming. There are some spam filtering programs that you can use if you are interested. There are free and paid ones. Unfortunately, we all get spam one time or another, that's why I created a dummy/junk email account for all sites that require a email and that I don't really trust.
Your log is clean.
To help prevent future spyware installations/infections, please read the Anti-Spyware Tutorial
http://www.greyknight17.com/spyware.htm#prevent and use the tools provided.
Are there any problems now? If not, you should be set to go.