Suppose my computer is compromised or has malware. Can the malware spread to my phone? If so, how? Has any malware been observed in the wild to do this?
Relevance: Some banks use two-factor authentication of online banking transactions; when you want to make a transaction, they send a confirmation code to your phone, and then you need to enter it into the web site to confirm. This is intended to protect against fraud by malware on the customer's computer, but if malware can spread from your computer to your phone, this protection looks less effective. Also, a number of web sites have started to use two-factor authentication, and they would be affected similarly.
Related: Can a compromised mobile phone be used to penetrate a desktop or server? asks about the reverse scenario.