Is there an Iphone key logger for non-jail broken phones? I would like to know if a key logger can be installed on a non-jail broken IPhone?

Thanks
In the practical sense, yes you can. You can use an exploit for the iPhone software to gain access to install the keylogger. If you want me to tell you how, I can't/won't.

On the nitpicky "theoretical" side - no, you cannot. If you use an exploit for the iPhone to gain access to install the keylogger, you could say that you have really jail-broken the iPhone. Thus you cannot install a keylogger on a non-jail broken iPhone.