Oh yes! Feel free to use old clothes for quilts! Just be sure to use interfacing on any knits (t-shirt material, fleece, streach denim, etc.) Try a medium interfacing and you should be good to go. See my avatar photo over there on the left that's the quilt top I made from my daughter's baby clothes! It's not much in the photo, but it gets more beautiful everday that I quilt on it.
Don't forget to cut off buttons (to make a button box, so you will never run out of buttons again), and any zippers, I've found the zippers from daughter's clothes work great to make pillows.