The most underused part?
(Small newsflash. The 800x480 pixel GD3 7" is now back in stock, and ready to ship. They look great, and work exactly like the original GD3 but with higher resolution. They are available in the Excamera Store).
If you've made any hardware design, then you probably wasted them. Our civilization is making them so fast we perhaps only use half of them. What component is it? The humble GPIO. There are dozens in a typical microcontroller, perhaps hundreds or thousands in an FPGA. Here I'll run through some ways of using GPIOs that go beyond digital input and output. The last one is a circuit I'm planning on using for I2CDriver.
Piezo double voltage driver
Tiny piezo speakers are usually driven with a single GPIO:
The speaker sees a square wave with amplitude VCC (e.g. 3.3 V) and generates an annoying beep. But you can also hook it up like this:
By driving the GPIOs with two square waves in opposing phase, the speaker sees a square wave with amplitude 2 * VCC, which is twice as annoying!
3-way sensing
This circuit, taken from Microchip's 2009 Tips and Tricks guide, shows the idea:
You can detect in software if a GPIO is GND by first driving it high, then making it an input and seeing if it quickly returns low. Similarly for VCC. I've found it works fine without the resistor and capacitor. There's enough capacitance in the GPIO and the circuit, and driving a microcontroller's GPIO the wrong way for a few nanoseconds is unlikely to damage it.
Analog output
Generating a pseudo-analog output with a 1-bit signal is a well-known technique. Almost all microcontrollers have a PWM capability, which generates a high-frequency square wave to approximate an analog value. You can do audio this way -- a generation of British people were subjected to a lot of it thanks to the ZX Spectrum. This is an excellent example - it's just a 8-bit CPU driving a single bit with some really clever software. Of course fidelity increases with frequency, though higher frequencies are tricky with microcontrollers. At around 50 MHz the quality of 1-bit audio is about the same as AM radio.On an FPGA or ASIC it's practical to use sigma-delta coding instead of PWM, which significantly reduces noise. Ancient Xilinx application note XAPP154 shows how to do it. Sigma delta coding is often presented in a confusing way, but really it's just the 1-dimensional equivalent of Floyd-Steinberg dithering an image.
Power supply
Low-current peripherals can be powered directly from a GPIO. Why would you want to do this? Two reasons: a reliable reset, and power down. This application note makes the case for adding a rock-solid reset to a peripheral by simply switching it off then on again. A GPIO hooked up to the VCC of the device will do this just fine with zero extra parts. While many devices have a low-power mode, entered by a special commandsequence, with the VCC on a GPIO, it all becomes very simple: you power it down by switching it off.
Programmable pull-up
I2C's signal lines need pull-up resistors. High-end I2C adapters have software enables for their pull-up resistors, which can be implemented like this:

For I2CDriver the three resistors are 2.2K, 4.3K and 4.7K. In combination, these can give a range of pull-up strengths between 1.1K and 4.7K, quite a reasonable selection for I2C.