GuizmOVPN is an OpenVPN GUI for the iPhone, it has designed to be easy to setup, configure and run, a background daemon runs the tunnel. GuizmOVPN is a premium paid for applet and it includes a 7 day trial period.
Unfortunately this applet can not be found at the official App Store and it requires a jailbroken iPhone, the reason why it can be found at the App Store is that GuizmOVPN needs to use a background process to keep the VPN tunnel active when the GUI (Graphical User Interface) is closed as well as running external commands to modify the network configuration.

GuizmoOVPN iPhone VPN applet