The communication methods that do not require joining the MFi program include cellular data to a server with a public IP, WiFi using a local access point, audio (FSK, etc.), BluetoothLE, Bluetooth (to keyboards and headsets, or at least devices capable of pretending to be such), and MIDI (via the Camera Connection kit). Perhaps also the display or LED flash and the camera (there appear to be a couple apps in the App store than claim to communicate via blinking in Morse Code).
General Bluetooth data, USB, serial and other ports on the bottom of the iPhone are off-limits to apps on stock OS devices unless you somehow manage to join Apple's MFi program, which appears to be not easy.