Symbian, for sure.
Windows Mobile, maybe too. Don't know how strict Microsoft is. Don't care TBH...
Android, if Qt runs in Java VM. Which it doesn't, as its not a native Java application. So no Adnroid either.
Apple won't allow competition for e.g. Cocoa Touch. They force you to only use their own APIs. That is why no App Store applications collaborate together. Therefore, I only see Qt for iPhone OS happening in jailbreak.