I don't believe in reincarnation of the psyche, or soul, as I don't believe in souls and believe that the psyche is made up of our bodies it can't keep on existing without our bodies.
I believe in physical reincarnation, though. When I die my body will lie in my grave and reincarnate into a million different things, worms, bugs, fungus, bacteria; whatever else eats my corpse. Then as they break me down into tiny little parts I will reincarnate into grass, trees, bushes. Other things will eat the bug-me or plant-me and I will become spiders, birds, and then predator animals who eat those, and so on – I don't need to lecture anyone on how the food cycle works – and maybe in many many years I will be incarnated into another human again, like I am likely the incarnation of many people before me, in some way.
It's why I don't like graveyards as they exist for us right now, with well cut lawns and little life. If I had a choice of how to be buried, I'd want to be buried under a tree, so the tree would would eat my parts and I would become it. Then those I leave behind could go to the tree and hang wreaths and flowers on it, like we do a headstone, and I would not be gone, not a cold, unanswering stone, I would just be part of something new.
Imagine if instead of the graveyards we have now we could have a forest, and we could wall from tree to tree and think "this is my father's tree, this is my grandmother's tree, and rhis is my grand-grand-uncles tree" and feel their bark and new life qs well as our own history and past in our very hands. I think that would be beautiful.