Yes this is possible, but it is not possible by cutting two USB cables with USB-A connectors (what is normally going into the USB on your motherboard) and cross connecting the data cables. If you connect the USB power lines on such a self made cable, you are likely to end up frying your on-board USB handling chip. Don't try this at home!
On most computer boards the chips handling USB are host only. Not only that but, it also handles a lot of the low level communication to speed things up and reduce the load on the CPU. It is not as if you could program your computer to handle the pins on the USB port to act as if a non-host. The devices capable, on the chip level, of switching between acting as a host and connecting to a host are few, as this requires a much more expensive chip¹. This is e.g. why intelligent devices like my smart-phone, GPS and ebook, although they all run Linux or something similar, do not allow me to use
ssh to communicate when connected via a normal USB cable.
Those devices go into some dumb mode when connected, where the host (my desktop system) can use its storage as a USB disc. After disconnecting the device uses the same interface as a host as to get to the data (although no cable connection is required, this happens internally). With that kind of devices even if Linux runs on both, there is no communication between the systems, i.e. the linuxes. This independent of a normal micro or mini USB cable connecting them to my desktop.
Between two desktop PCs the above is normally impossible to do as you would require a USB-A to USB-A cable, which is is not common (as it would not work with the normal chips that are driving the connections anyway).
Any solution doing USB to USB with two USB-A connectors that I have seen, is based on a cable that has some electronics in between. (much like a USB → Serial plugged into a Serial → USB cable, but then all in one piece). These normally require drivers to do the transfer, although you might be able to use UUCP or something else over such a cable, like you would over a "normal" serial port. This probably requires inetd and proper configuration to login on the other computer as well.
¹ The only device I have that is software changeable in this way is a Arduino board with exactly such a special chip. Just this chip made the board twice as expensive as a normal Arduino board.