How can I make a simple 3D line with Matplotlib?

I guess, you want to plot 4 lines. Then you can try

for i in range(4):
    ax.plot([VecStart_x[i], VecEnd_x[i]], [VecStart_y[i],VecEnd_y[i]],zs=[VecStart_z[i],VecEnd_z[i]])

As Nicolas has suggested, do have a look at the matplotlib gallery.

The gallery is a great starting point to find out examples:

http://matplotlib.org/gallery.html

There is an example of 3d line plot here:

http://matplotlib.org/examples/mplot3d/lines3d_demo.html

You see that you need to pass to the ax.plot function 3 vectors. You are actually passing list of lists. I don't know what you mean by the Start and End sublist, but the following line should work :

ax.plot(VecStart_x + VecEnd_x, VecStart_y + VecEnd_y, VecStart_z +VecEnd_z)

Here I sum the sublist (concatenation) in order to have only one list by axis.