What banks also own insurance companies?


Are you referring to banks owning agencies? BB&T and Wachovia own insurance agencies. BB&T has done very well with their insurance departments. In North Carolina there are several community banks that have their own insurance agencies.
Depends where you are.

In Australia banks aren't allowed to own insurance companies. They can sell insurance but it has to be underwritten by an actual insurance company.
State Farm comes to mind.
I don't know about that, but I know some insurance companies own banks - just not the other way around. United Healthcare owns banks.

Answers:
Citigroup is the first one that comes to my mind, Primerica.