For me, it depends on what type of use the end item will get. As an example, I'm going to make a long picnic table cover (157inches long and 40 inches wide)with red, green and white fabric. These are the Basque flag colors. Since it will be washed frequently after it is finished I will prewash all of the fabric for color and shrinkage just to make sure. Yes, either surge the edges or run a machine stitch all the way around the cut edges. I learned this the hard way; I took a large fabric piece out of washer and spent the next hour trying to get it untangled from all the threads that had come loose and wound themselves all up and down the fabric.
Purses, wall hangings and anything else that probable won't be thrown in the washer I don't prewash.