Keyloggers (often malware, so not intentionally put there by some hacker) download the passwords for your FTP sites, and alter some of the pages on the websites you have FTP data from. They will use your websites to send spam.
The spammers can use "clean" websites as relays to send spam, and move on to a new one, leaving the site owner to deal with the consequences. Likewise, they can send out spam using hacked individual accounts. The advantage here is that people are more likely to open an email from someone on their contact list, and these emails are often whitelisted.