Regular t shirts (fruit of the loom, jerzees, Just my size, Hefty t's etc) will curl if cut in either direction. If you cut them from the bottom hem of the shirt toward the shoulders/neckline, the shirt will curl with the right side out. If you cut them parallel to the bottom hemline, they will curl with the wrong side out. For most shirts, the way it is curling doesn't matter for the finished product, but if you have spray dyed your shirts, or the color isn't the same on the outside and inside of the shirt, it could make a difference to you. Double knit shirts, 'better quality' t's and some 'polo' type shirts will not curl.

To answer the question above about age of shirt and the curling effect. I've used shirts that were 20 years old or more, and thin from use, they still curl up nicely, and haven't uncurled over time, if anything, they curl more.