I've often wondered whether this'd be particularly suited to Allegro. Has anybody written anything that displays output corresponding to audio input events?

The first thing that came to mind was the usage of ALLEGRO_AUDIO_STREAM, but after looking at the manual, I can't see that it (or anything else within the audio addon) concerns the buffering of audio from a stream external to the program, or any kind of complex DSP for that matter.

So, could anyone recommend a C library for reading and processing audio input streams? Or is there a way to do this with the Allegro audio addon that I'm missing?

I don't think that Allegro is what you're looking for.

What you need is to be able to read the sound hardware buffer as it streams real time, or shortly behind. This means OS specific code. A library like FMOD probably already does what you need sans the visualization code.

I've also found the Juce library, which has this example, which appears to demonstrate the handling of input streams (even via ASIO) and built-in FFT.

(it seems to provide its own graphics library too, though I'd obviously prefer Allegro)