Well, I do wonder exactly what operating system you are using. It seems most likely to me that you are using some version of Windows from your post. Paranoia aside, a person with a dial-up connection is probably not attractive enough to need more than a well patched system, an up-to-date antivirus system, and one of the free software firewalls, such as ZoneAlarm. These will provide reasonable protection against e-mail stuff and malicious popups. The firewall will also provide warning of any outbound traffic that you don't want to authorize.

If you have an always on, high speed connection, you may be attractive to Warez folks, etc. One of the basic precautions in this case is to shut down services you don't use, such as the ISS. Be especially careful of allowing anonomous users write priviledges if FTP is up. If you do run ISS, be sure to get the lockdown tool from Microsoft (free).

You may also want to do some enhanced surveillance of your system (how much is up to you and depends on the time you have to spend -- it can be an interesting activity in terms of learning about your computer.) In Windows 2000 or XP Pro, you can audit system, security, and application events. The settings to use and the meaning of the logs can take a little time to understand, but you will be able to see interesting events. If you do use ZoneAlarm, you may want to download ZoneLog from Dshield.org. It is helpful for interpreting ZoneAlarm logs and also can provide a report of activity to Dshield, who track such things.

There is a lot one could do, but an up-to-date system, an anti-virus program, and a firewall will address many issues. Ad-aware, etc. are also helpful, but you have to decide how safe you want to be.