having your passwords stored on your system is actually LESS secure then typing it in every time
The problem is that "saved" passwords are often accessible from the application that saved it once you have logged on to the computer. The various programs inherit their security authorizations from the user. So if you can use your email or web browser without entering a "saved" password, a trojan that installed itself under your account can usually do the same.
Most email spamming is done by use of trojans setting up netbots, that will use your home computer to actually send mail on the accounts available to it. In that case the trojan will often use your home computer address book as a source, or sometimes harvest it to send more live email addresses to the botmaster. It is not clear in the present case if that was the method used, or if the actual email account was hacked at the server. In the latter case, the mail can be sent from another computer that is logging on to your compromised email account at the email server using a stolen password. It makes a difference in deciding if your home machine is compromised, or just your email account. If only your email account password was stolen, then all you need to do is change the email account at your mail providers site. If your computer is compromised, then you need to do a serious cleaning which may involve a re-install of everything in the worst case.
Another possibility is that neither your computer nor the email account has been compromised, but that your email address is being used to spoof email from an unrelated source. Someone whose home computer includes your email address in its address book may have been compromised, and your email address harvested. From there the spammer just makes it look like the email came from your address.
Keyloggers are a more sophistocated and labor instensive method of stealing a password, that the hacker can later use from his own computer to access your password protected online account. If someone has a working keylogger on your machine, he would be foolish to use it to steal an email account password and start spamming. He would wait for your online banking or credit card information and start sending himself checks or merchandise .