I made a small "blankie" for my then-toddler. It is cotton on one side (with a Minnie pattern) and fleece on the other. We had the characters autograph the cotton side with a Sharpie pen. We've taken it on two WDW trips (when she was 2 and 3) and got it autographed both times. We're going again in a couple of weeks (she's 4 now) and I'm not sure if we'll take it again or not. In any case, she still has it as a treasured possession, and it's much more useful than an autograph book! It's stood up to lots of washings, too.
My big kids have gotten hats autographed before, and I brought a plain canvas tote bag one year. I brought an embroidery hoop, and just kept moving it around to get the autographs in different spots.
One trip we took quilt squares and got them autographed individually. I intended to sew them into a quilt but have never gotten around to it. The blankie idea worked out much better.