I do both, wash and not wash, depending on the quilt.
If it is a quilt for show, I always wash so I can block the quilt to make it hang perfectly.
My method: Wash your quilts in the washing machine BUT don't agitate very much at all. I have a top load washer so I fill with cold water and let it soak for a while. Then I use my hands and squish around a little. I let it agitiate for only a minute or two. Then I let it rinse and spin out etc.
What is hard on your quilts is the agitating, not the spinning so agitate as little as possible. After the quilt is spun out, I VERY CAREFULLY lift the quilt and put in the dryer for about 5 minute increments and rearrange when the buzzer rings. Always be careful when handling that wet quilt. This is when it is fragile from the water weight.
Once the heaviness of the quilt is gone, usually about 20 minutes, I take it out and lay it flat on the floor and let it dry the rest of the way. If the quilt is for show, I pin it to the carpet to block it. If not for show, I just let it dry.
What do I use to wash my quilts? I use a small squirt of Dawn dishwashing detergent in the washer. Small so you don't get too many suds.
Another trick to make that quilt nice and soft: use a lot of fabric softner in the washer and a dryer sheet in the dryer. This makes even a quilt that has been machine quilted to death nice and soft. It also smells wonderful!