The DDC interface, which is an I2C bus that allows for bidirectional communications to read EDID data, so you know what you are plugging into. Hot plug detection via the HPD line, so you can tell if you are plugged in or not. Embedded 5V power, very useful for conversion dongles, ethernet, probably more things I forget.
HDMI has a lot of pins, which makes DIY cables difficult, however they are useful.