I have one custom made device for measuring current. This device can be connected to PC and communication is done over USB. It is based on FTDI chip. I have application writ
I think there's currently only one properly maintained library for serial USB communication and it's felHR85/UsbSerial. It supports several USB chips including FTDI (see Devices Supported).
Unfortunately mik3y/usb-serial-for-android seems to be dead.
And no, you don't need to root your device for connecting to and communicating with a USB device.
EDIT: We have a maintained fork of mik3y's library. See kai-morich/usb-serial-for-android
EDIT2: It seems that all of these libraries are maintained again, mik3y joined forces with kai-morich and they are working together.