Neat idea, but is imagine on your return flight, the 'extra baggage" charges would be pretty steep!

Thanks to all, for the info. I was dreaming about creating a pick up service for hard to find parts. My plan was to vacation,  1-2 months in Europe, buying parts to resell, and importing back to the USA. I had hoped this would pay for a portion of my vacation.
Jay

Building a car from parts would probably not pay, but bringing in parts is easy. Sometimes I have things shipped to my daughter in the US and then I pick them up for my trip to South America. you pay 2.5% duties, but obviously have to have everything declared in detail.

Jay,
come to NY and you can fill a box truck from my two car garage. Lots of parts. PM me from my profile. 
mike

I think the short answer is 'no, not worth it'. If you are thinking of building a car from parts, it would be a long, slow, expensive way to do it. Shipping, handling, brokers, duty etc. would probably cost more than the parts are worth - sometimes the case for brand new parts. If you are thinking of stocking and marketing used parts, the outlook is dimmer: if someone needs a part, they are more likely to want to use a new part, which is readily available.

 The reason I am inquiring about this is, I recently traveled to Italy. During my travels I saw may Inno's, old Fiats Renault's and many older "classic" cars, not normally seen in the US. I suspect that there would be a decent market, for these old car parts here in the US.        Yes, I know that many people buy parts from eBay ect.  I am wondering about is importing a large amount of parts, is it worth the effort?

Ask me for what you are looking for. I have 45 years of accumulated parts.

NO..  each part MUCH be labeled and listed on the bill of lading and you have bill of sale AND PROOF of purchas such as wire transfer or CC receipt  and have a DOT marking.. on EVERY part..

Keith & Deb
  What would the US customs agents have to say about a trailer load of "junk mini" parts?

There are  a lot of bits and pieces lying around in garages and storage sheds in North America... 
No need to bring anything from over the pond. Just post a wanted ad and see how fast someone will come up with what you need.. If you are willing to come to Canada there are plenty of left over cut up Japanese Minis... 
Deb

There has been much discussion about the problems of importing cars into the US. What would the potential problems be, for importing only parts. I am talking about junk yard engines, front sub frames, maybe body shells. Ect.   Of course you would need a "connection" across the pond, to find the parts and pay for a shipping service.  Anyone have any thoughts.