I have something like this which is very very useful:
generalEditText.getBackground().mutate().setColorFilter(getResources().getColor(R.color.white), PorterDuff.Mode.SRC_ATOP);
where generalEditText is my EditText and color white is:
<color name="white">#ffffff</color>
This will not remove padding and your EditText will stay as is. Only the line at the bottom will be removed. Sometimes it is more useful to do it like this.
If you use android:background="@null"
as many suggested you lose the padding and EditText becomes smaller. At least, it was my case.
A little side note is if you set background null and try the java code I provided above, your app will crash right after executing it. (because it gets the background but it is null.) It may be obvious but I think pointing it out is important.