What's the difference between these three words?

I think is the most formal and I reckon is the least.

I reckon is hardly used at all where I live.  I associate it with the southern U.S.  It's more similar to I guess than to I think.

The usage of I think and I guess can be quite different. 

You use I think to express an opinion.  It may have a forward-looking, positive feel.

I think high fructose corn syrup is responsible for obesity in children.
I think we should collect signatures so we can get this law repealed.
I think you'll do very well on your exam.

(I would not use I guess (I reckon) in any of the statements above.)
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You use I guess to give your estimate of a situation.  It can express powerlessness to do anything about the situation as well -- or at least the idea of resignation to the situation.  It's somewhat more backward-looking.

I guess I've lost the lottery again. I don't have any of those numbers.  (sigh)
I guess you'll have to start over, now that you've ruined that batch.
I guess I must have got the wrong number because the call's not going through.

(I would not very likely use I think in any of the statements above -- certainly not with the first of the three, although possibly for the third.)
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There is some overlap, however.

CJ

My hometown is Yokohama and I still live here.

Come by and see me in Uchikoshi sometime.

Omo wrote:

"I think", "I guess" and "I reckon"(not the meaning of to calculate) share the almost same meaning, I think. If so, what kind of nuance do they have?

Showing my age, I associate "reckon" with cowboy movies of the 1940's and country&western music: "How it beckons, and I reckon/ I would work for any wage/To be free again, just to be again/ Where the bloom is on the sage." (Gene Autry)