How do you root Android phones?

Are there any known Android malware apps in the wild that can self install on retail Android phones with default settings, and root and infect them? If so, what are they?

• Malware that installs on devices already rooted by the owner doesn't count.

• Answer:

  No. At the bare minimum you need, 1. Some way to take control of a system app by executing your code [most likely via taking control of the browser] 2. Make user ex