I've used sheets for backing a number of time successfully. Always pre-wash. Also, as a side note, I recently learned to always put the 'nubby' side of batting UP so that the smoother side is against the backing because as the machine needle comes into the fabric, it sometimes pushes the nubs out the back.

I normally use quilters cotton, but recently tried fleece after some prompting by a friend. It was easy to machine quilt, but left a lot of fluff in my machine which I had to clean out more than usual. Made a nice soft and cuddly backing though, and I haven't had any problems washing it.

I guess it comes down to whatever you like best!.

you can piece your backs with left overs, you can purchase wide backings, you can purchase wide muslins, you can use yardage of cotton fabrics piecing to make it large enough, you can use fleece, you can use flannel, you can use minkee...
and some people do with good results...use sheets.

if you use a solid (muslin or any solid color) every stitch will show...
if you use a white on white or any print- the stitches will not show up so well and every mistake will not be (on display)...the beautiful quilting will still be there but every little boo-boo will not be jumping out at you.
if you use flannel- pre-wash- it shrinks alot-
if you use a batik or hand-dye--pre-wash they tend to bleed.
if you have mixed fabrics in the top- make sure everything (including your choice of backing and batting) can be laundered together.
(batik's are normally a tighter weave than the other cotton's we use--about the same as a normal quality sheet)so...if you use batiks...no reason to be afraid of sheets...as with all fabrics. there are different weights/weaves and qualities....
nothing is carved in stone.