Just bought a Logitech F310 which works great with the Raspberry Pi. No need to install any driver software either. I needed to reboot a few times with the controller plugged in for it to first be recognized, but now it works every time. Also, surprisingly I needed to set the switch to “XInput” mode for it to work. DirectInput did not work for me.
This is on the latest official Raspian image with only Retroarch and Emulation Station installed.