Can I barter cigarettes or jeans or any other American product, for locally produced products in Belize, Honduras, or Mexico?

I suppose you can try. But a better question would be, why would you want to? Most vendors, I would think, don't want your junk, they want your money. Like you observed in the other post on cruises.

Maybe, if one had a black market business in the aforementioned items, it could be useful, cut out the cash conversion portion of chain.

Not likely. That entire concepts is decades out of date.

Why not take some wampum while you are at it?

Definitely outdated in most of Mexico... although still very popular in Cuba.
Most Mexicans are very proud and probably dress as well as you do !

NFL & US Baseball tees/hats stil lhave trade value. Also Golden State stuff has been hot until this last playoff.

Stew, I don't believe for a second you've been bartering t-shirts and hats for handcrafted goods. Those are trinkets you give away to kids. I know you travel on a budget, but...

Yes, you can in some instances. As Stewbear said, there is a demand for official sports memorabilia for popular teams and used or new US made jeans. Course many other countries in the world seek out the same things.
Fact, as requested, I'm bringing back a few sports hats and T-shirts for my return trip to Mx.
In regards to cigarettes, I actually used to bring a guy that we rented from years ago Vantage cigarettes. He'd take the cig price off our room fee. That was a long time ago, though. Cig prices in Mx are much less than in the US so I imagine that there may not be a demand.

"US made jeans" where would you find them ?

No I do not barter any thing anywhere But I have observed others doing so at a number of beach locations including Puerto Vallarta & Zihuatanejo.

Sorry but I have never once witnessed people bartering cigarettes or jeans for hand crafted items in Puerto Vallarta.

hyattlodge, Just got a message about bringing an electronic device back down to Mx. Forgot about those. Mxs prefer US electronics over their own.

"US electronics" where do you find them, same place as "US made jeans"?

Actually Suze I had (Have) a friend in PV who detested Mexico made cigs who I took a carton of her favorite brand down each year but not to barter just as a gift however others would barter food at her cafe for them with her. Fortunately she has long since quit smoking those cancer sticks.
I also have seen others barging tees/caps on the beach in PV & the other fore mentioned spots.

Well of course. I have brought specific items upon request of a friend. Most recently my landlady couldn't find her favorite kind of Earl Gray tea in PV and asked me to bring a few boxes from Seattle.

But that is not randomly packing in packs or cartons of cigarettes to barter with strangers (per the question of the OP here)!!

Thank you everyone