It is important to keep your email address secure. Why? Because often times, your email address is a gateway to many other things that you do online. For example, if you have a Pay Pal account, where does Pay Pal send notifications about your account? Directly to your email address.
Email spam is not necessarily harmful. Many times, spam is just junk mail from companies who are trying to sell you something. The thing is, it's annoying getting spam.
How do these companies get your email address? Many times, illegally. Large lists of people's email addresses are sold by companies and bought by other companies quite often. In turn, these companies use the email addresses to try and sell their products.
You can receive viruses and malicious spyware via email. However, most of the time you need to initiate the spyware in order for it to damage your computer. For example, simply previewing an email will not infect your comptuer with a virus. But, if you open an attachment, it could self extract to your computer and load a virus.
The best thing to do to prevent stuff like this is simple. Do not open emails from people that you don't know. If you are using an antivirus program, many times you sync the program with your email account to scan all email attachments. This can stop threats from being installed.