What malware has actually affected Jailbroken iOS devices? Are there examples of malware that affects jailbroken iOS devices that doesn't require installation of shady packages (e.g. something that can compromise a device just by opening a PDF or visiting a site)?
I hate to say it, but in all my years of jailbreaking I have yet to see any type of malware have any real impact on the iOS community. Sure there was the infamous SSH vulnerability, but that was patched rather quick. That's the beauty of jailbreaking; we don't have to wait for Apple to release a fix. Most people fear that jailbreaking is insecure and puts your device at risk. That's far from the truth. My favorite example is the jailbreakme.com PDF exploit for iOS 4.3.3. At the same time they released the exploit, they pushed a patch to Cydia. As soon as you jailbroke, you were advised to install the patch, so that your device could not be further compromised. It took Apple a lot longer to implement and roll out their fix. In that situation, it was better to jailbreak than to not, because unless you had the patch, someone with bad intentions could have abused the exploit and done anything they wished with your device. Sure, you can be careless and install some malicious software, but most of the time it's the user's fault, because you always should be careful with what you do in a limited-regulation environment. As a final answer to your question, there were a few PDF exploits that were triggered merely be visiting a website (jailbreakme.com), but those vulnerabilities were never used for evil.

Edit: Another malware example has popped up, but it's not specific to jailbroken devices; it can remotely jailbreak any device without user interaction. This is the first time we've seen a remote jailbreak being used in the wild for malicious use. Apple has already patched it - they patched it quick. But the jailbreak community took a few months to patch it.