I would like to be reincarnated into a different species, one that has so little perception of the world that the thought of death and an uncertain future is not on my mind. I would like to no longer ponder the meaning of the world nor worry about trying to solve man-made problems. Turn me into plankton and let me soak up the sun until I cease to function.
Alternatively, if I could save all that I have learned and experienced in this life, then I would like to be reincarnated back to my life and do things differently. Just one more try to appreciate what I didn't at the time.
It's also been wonderful reading all of these different answers. Some of them have reminded me of the Pythagoreans and their concept of the "wheel of birth" where the immortal soul is trapped in transmigration from one existence to another. They believed through purification and the pursuit of knowledge through mathematics could one liberate themselves from the wheel.