It seems there are some projects which make the raspberry pi into a minimal logic analyzer with some hardware. Here are the links:

1. http://tuxbabe.eu/raspalyzer.html
2. https://github.com/richardghirst/Panalyzer
3. https://www.raspberrypi.org/forums/viewtopic.php?f=37&t=7696

There is another project which uses a PC based oscilloscope to achieve a similar result:

http://codeandlife.com/2012/05/16/worlds-simplest-logic-analyzer-for-5/

These projects have a max sampling rate of 1us (i.e 1MHz) which is not enough for most uses. I think the bottleneck might be the GPIO speed rather than the processor or software. To get higher sampling rates, the GPIO internal circuitry should be able to reliably read the incoming data. Here is an article showing the GPIO benchmark results for outputting bits:

http://codeandlife.com/2015/03/25/raspberry-pi-2-vs-1-gpio-benchmark/