I recently unpacked some quilts that I had put away and realized how wrinkled they got in the containers! I had to throw them in the dryer and fluff them a bit to make them presentable.
Once they were beautifully flat, I realized I had to get them back into the box! So, yes, I refolded them. BUT, I refolded all them on the bias. (What?)
I highly recommend that you try this when putting quilts away for a while. The bias creases less than the straight on grain and your quilts will love you for it! So will you when you're ready to dig them out of storage!
Helpful hint, though: Be sure to never put quilts in attics, basements or cedar chests. They can get damaged from the humidity! Short-term storage should be in a cloth bag or pillow case, bias folded, in a closet or under the bed.
Long-term storage should be in an acid-free box, bias folded with acid-free tissue paper between the folds.
The absolute best storage is on a bed! Layer your quilts on a spare bed, if you have one. No folding necessary! Then you can rotate them, putting different ones on top periodically and enjoy your quilts.
Here's how to fold on the bias: