Did "Unsolved Mysterys" ever have a segment the issue of Reincarnation?

yes

Yes.
I don't remember any names, but I remember the woman who had---or claimed to have---dreams of being a young woman in the 19th century. She said she was the reincarnation of the young woman. She did some research and found out the woman was real. For some reason, the last name "Green" ("Greene"?) is ringing a bell. Anyway...... there was also a man that believed he was the young woman's reincarnated lover. He originally died from drowning in a lake, if I'm remembering correctly.

I'm sure someone else here can give you more details.

her name was georgia rudolph I believe, and she believed she was reincarnated as the girl in a small ohio town along the ohio river. The segment is very interesting and is on the psychics box set I believe.

Not one of my favorite topics, but there have been a few segments focusing on reincarnation...

* Georgia Rudolph who believed that in a past life she was a young girl who commited suicide around the turn of the century.

* A woman who believed that she was a soldier killed at Pearl Harbor in one of her past lives.

* A man who believed he was killed in some type of war-related conflict in a past life - this was on the season 6 premiere, but I've never actually sat through the whole story and come to think of it, I can't remember seeing the story on Lifetime either. Hmmm. The episode guide says the guy was from Glendora, California.

* A story about young children who can remember details about past lives. I remember one boy having a fear of fireworks and loud noises. Hypnotherapy sessions revealed a past life where the boy was a soldier killed during the Civil War.

* A man who believed he was killed in some type of war-related conflict in a past life - this was on the season 6 premiere, but I've never actually sat through the whole story and come to think of it, I can't remember seeing the story on Lifetime either. Hmmm. The episode guide says the guy was from Glendora, California.

Was that the guy who met "Bokey" and his wife, from Alabama I believe? I recall something about how the guy did a lot of things that the guy in his previous life did, like exiting the house through the back door and liking the end pieces on loaves of bread. He also recalled the courtship of a lady.

Was that the guy who met "Bokey" and his wife, from Alabama I believe? Someone had Bokey as their avatar, but I think it's been an eternity since they've posted. I recall something about how the guy did a lot of things that the guy in his previous life did, like exiting the house through the back door and liking the end pieces on loaves of bread. He also recalled the courtship of a lady.

Yes, that was Bruce Kelly, I believe.

'Bokey' was the old man he met in Alabama?

On the Psychics Box Set.

yep, Bokey was the older gent.

I believe Bruce Kelly for some reason. I don't know..