When Benjamin Franklin was 22, he drafted an epitaph for himself which clearly shows that he believed in reincarnation:

Body of B. Franklin,
Like the Cover of an Old Book,
It's Contents Torn Out
Stripped of its Lettering and Gilding,
Lies Here
Food for Worms.
But the Work Shall not be Lost
For it Will as He Believed
Appear Once More
In a New and Elegant Edition
Revised and Corrected
By the Author

In 2002, PBS broadcast a special about Franklin which included an actor, playing Franklin himself, introducing the series. In it, the actor says:

"I've had a very happy life. So much so, that I'd have no objection to living it all over again! Well, perhaps I'd correct a few errors I made the first time 'round. But since repetition is impossible, the next best thing is to remember that life. And to relate it to you."

You can play the video clip here.

The sentiment expressed in the introduction is very close to the epitaph--it even looks to me as if the actor playing Franklin is paraphrasing the epitaph, but turning its meaning around backwards so as to make it appear that Franklin actually disbelieved in reincarnation. This is just one of the ways that society continues to marginalize this concept. Franklin is praised to the skies in the introduction to this documentary, as a statesman, inventor, writer, and signer of the Declaration. But his belief in reincarnation is not only conveniently omitted; it is actually reversed. Had they let the actor speak Franklin's actual words, PBS's entire audience would have had to come to grips with the fact that such an influential, intelligent and thoughtful person accepted a concept which they believe is nonsense.

By the way, note that in the epitaph, Franklin mentions the "Author". That means that he believed in both God and reincarnation at the same time, while the actor mentions neither.

Addendum 9/6/14
I appear to stand corrected as regards the PBS quotation of Benjamin Franklin. Just now reading his memoirs in "The Works of Benjamin Franklin," written in old age, I find that in the introduction, he says substantially what he is quoted as saying in the PBS special:

When I reflect, as I frequently do, upon the felicity I have enjoyed, I sometimes say to myself, that were the offer made true I would engage to run again, from beginning to end, the same career of life. All I would ask, should be the privilege of an author to correct, in a second edition, certain errors of the first. I could wish, likewise, if it were in my power, to change some trivial incidents and events for others more favourable. Were this, however, denied me, still would I not decline the offer. But since a repetition of life cannot take place, there is nothing which, in my opinion, so nearly resembles it, as to call to mind all its circumstances...

I am not, however, prepared to concede that this proves he disbelieved in reincarnation in his later years. I smell a rat someplace, I'm just not sure where it is, and it would take a lot of research to run it down. Because of the extreme similarity in the wording, I would say that a simple change in beliefs, from youth to old age--the obvious conclusion--is actually the least likely explanation. It could be that the epitaph is spurious, or has been edited to suggest reincarnation. It's equally possible that the editing of the autobiography took place, not with PBS, but with the original editor--whose name I cannot find in the book--in 1825. Any sentiment suggesting reincarnation would have been even more objectionable then, than it is, now; and constraints against such editorial "adjustments" might have been less. This book of Franklin's memoirs (i.e., the edition I downloaded from Archive.org) would have been published 35 years after his passing. One would have to find the original documents for both quotes, if they exist.

A little more research yields a different publication of his memoirs, which includes a letter from Franklin to George Wheatley dated May 23, 1785, when Franklin was 79 years old. At this time, he clearly seems to believe in both God and reincarnation (his logic precluding the explanation that he was expressing a belief in resurrection). Note, once again the similar language as regards the "new edition." If, as it clearly seems, he was expressing a belief in reincarnation with language similar to his youthful epitaph, at age 79, I'd say the anonymous editor of "The Works of Benjamin Franklin," on which the PBS program apparently relied, must have fudged:

And when I observe that there is great frugality as well as wisdom in his works, since he has been evidently sparing both of labour and materials; for by the various wonderful inventions of propagation, he has provided for the continual peopling his world with plants and animals, without being at the trouble of repeated new creations; and by the natural reduction of compound substances to their original elements, capable of being employed in new compositions, he has prevented the necessity of creating new matter; for that the earth, water, air, and perhaps fire, which being compounded from wood, do when the wood is dissolved return, and again become air, earth, fire, and water; I say, that when I see nothing annihilated, and not even a drop of water wasted, I cannot suspect the annihilation of souls, or believe that he will suffer the daily waste of millions of minds ready made, that now exist, and put himself to the continual trouble of making new ones, I believe I shall in some shape or other always exist: and with all the inconveniences human life is liable to, I shall not object to a new edition of mine; hoping however that the errata of the last may be corrected.*

One may still ask, therefore, why the PBS "Franklin" didn't say that!--SS

*"Memoirs of Benjamin Franklin Volume 1," By Benjamin Franklin, William Temple Franklin, William Duane, 1834, pg. 589