It's not very much fun for me, but I don't believe in anything magical. I don't believe that I was born to fulfill a certain purpose, or that the universe metes out happiness fairly, or that our souls are more than what's encased in our skulls. So I find it hilariously fun that I've come to believe in a kind of reincarnation.
Reincarnation is you coming back--existing again--in some form or another. To settle your beliefs about reincarnation, in my view, there are two things you need to decide:
(1) Who is "you"?
(2) How often does "you" happen?
The first question is the tricker one to answer, because we have no recourse to math.
Traditional adherents to various beliefs in reincarnation have universally allowed for a reincarnated person to be something other than an atom-for-atom re-instantiation of the person before.
Every belief in reincarnation that I've heard of allows for people to come back with different genders and hair colors. Buddhists allow for us coming back as sheep and dogs, and the Sikhs had one guy come back as a book.
I wouldn't feel very much like myself as a book, but I'd tolerate some differences between the me who writes this thing and the Next of Ken. If I were to wake up tomorrow with most of my memories gone and big tits, I wouldn't consider it the death of Ken Before. You may have a different threshold for your own you-ness. Some of my family grieved my grandfather as lost after his brain surgery.
The calculus of you-ness can vary so drastically that at one extreme you can identify your pattern with every living person, so that they are all sufficiently "you" to stand as your continuation, and your death doesn't matter as long as someone else stays alive somewhere (man MDMA is cool), and at the other extreme we can speak of a lost you-ness inside the span of one lifetime.
If you draw your you-circle very widely, you can be assured of your reincarnation, because your incarnations are already living out their overlapping lives all around you. If you draw a tighter circle, though, I still believe that there's hope.
If the universe is infinite (it isn't) and random (it is), then as a logical consequence, every thing that can exist does, somewhere. In an infinite universe, the dice would be rolled so many times as to guarantee another atom-for-atom earth, complete with an exact you reading this exact blog post. (Max Tegmark's math says that this mirror you is about 1029 meters away.)
But even if the universe isn't infinite, it's vast. If you draw your you-circle like I draw mine, you've been around a few times. Maybe sometimes as a girl in Iceland. Maybe sometimes as a squid overlord on Zebulon. There have been people who think and feel like me, who feel as me as I feel--much more than the Dalai Llama feels the same as his alleged past selves. With enough rolls of the dice, it's even likely that some of my incarnations have had false memories of each other's lives.
And so I've come to believe in a kind of reincarnation. Incidental reincarnation.
And yet it's nothing special. There are no magical levers, or god-made plans.
Like the galactic spiral on a seashell, I am just a pattern that the universe tends to repeat.