I have been looking into this extensively the last few months. Few things first:
1) You cannot re-import from Canada, UK, Germany, etc. This would actually be MORE difficult than shipping it in as piece parts.
2) R33's are the only full cars legal to import now. HOWEVER they have to go through a RI (registered importer) and have to meet FEDERAL compliances; DOT, NHTSA, EPA, etc. Currently no RI's are offering this service. This means that as of right now, there are no federally legal cars being imported. Word on the street is that Takara Motors out of Georgia is working on this, however I have heard nothing but complaints about slow staff and broken contracts from them recently. If you are thinking of becoming an RI, understand that your total cost to do this would be roughly $100,000 for the mandatory testing (set up, not per vehicle).
3) Regardless of how we try to fool ourselves, this is fraud. It is a reassembled vehicle, not a kit car. If you get in an accident, your insurance company may reject your claims and find you 100% culpable.
4) The DOT knows these cars. Its possible that you park it at night and the next morning wake up to see your car gone and a large ($50k, I think) fine waiting for you. You are defrauding the DOT, EPA and customs (which is the big no-no right now).
5) Since this is defrauding the Federal government, it is possible that if you ever sell the car and the insurance doesn't cover it, you could still be found in fault.
Now, the good news:
1) Sans California and some of the South Eastern states (New Mexico and Arizonia come to mind, but I may be wrong) you can get away with it 99% of the time. Most states will either issue a state ID number on the car or a VIN number. The State Patrol will do this(in most states). So if you know someone in the SP, you practically are guaranteed.
2) Most states will have some of certification be done. In Washington state, I would need the speedometer in MPH, ensure that ALL (not just windshield) are DOT stamped glass, and make sure the bumpers are SAE conformed. Glass and bumper are already there, but for WA, I would need to convert the speedo.
3) Progressive Insurance does insure them registered as kit cars after the model year they are, and they have paid out claims thus far. However, BE HONEST WHEN REGISTERING THE CAR. You are allowed to import piece parts, so don't lie about it, that can just get you in trouble.
4) Once you register the car, most states will allow transference of title into them, giving you substantial retail value.
5) Make sure the exporter will de-register the car, and try to find out when the last shaken inspection was. De-registered will flatten out most bumps in the registration process, and if it was recently shaken inspected, you have a pretty good trust that the car will be good.
Final thoughts:
If you import it as a kit-car, it will be a grey market vehicle for its life. There is always the chance that the impounding and fines will be levied; however I haven't heard of this ever happening. Also, if you know anyone in Florida or Georgia that would be willing to do the import/registration for you, take them up on that offer. Those states will basically register anything with 4 wheels and an engine.
I had a friend in college who was from Florida(now lives in Cali) and he imported from
http://www.japan-partner.com/ around 2004. He was t-boned in 2005 and Progressive paid for the car. He was routinely pulled over for being a RHD vehicle, so make sure you have ALL of your paper work.
If you end up going through with it, keep everyone updated. My buddy imported his 92 GTR with under 100k kilometers and got it completely legalized for just under $9k. Of course, now I am thinking I would rather spend that 9k to get a 300ZX TT and not have all the hassels, but good luck.