Here is one idea for reusing which is to cut the t-shirt into strips to make yarn for knitting.
From Instructables, sewmargaretsew details how to make the "fastest recycled t-shirt tote bag" promising that "With just two quick seams and some fast cutting---you are finished!"
On Etsy, lilblueboo has a tutorial pattern for sale to show you how to recycle t-shirts into an adorable dress.
For the t-shirts you would like to preserve, there are patterns for making quilts of them and there are plenty of people on Etsy such as prettythreads (whose quilt is shown below) who will make one for you.
I particularly like this style because of the way it is top-stitched. Many of the other t-shirt quilts I have seen are merely blocks sewn together. The meandering stitch used on the top of this one makes it look more like an old fashioned quilt.
DIYIdeas has a tutorial to teach you how to make a scarf from t-shirts and a pillow.
Hmm...looking at this scarf, I'm thinking that a few of these sewn together would make an interesting throw. See the scarf video here.
This is super easy to do. See the video tutorial here.