I believe the replies above are referring to the yearly registration fees, not just the first year. In CA, at least right now, the yearly "tag" renewal fees are based on the purchase price (or value, if received as a gift) of the car when the new ownership title is issued. Then, as mentioned above, the CA DMV has an automatic depreciation rate, so each year this yearly renewal fee will go down a (very) little based on this depreciation schedule. I haven't heard that CA will change this from "purchase price" to "market price", but it seems unlikely since the "purchase price" method is so tightly connected to this system now. As mentioned it is not uncommon for an owner to have to pay thousands of dollars a year just to get new tags.
But, for anybody in CA who is not aware, CA does have a specialty plate called "Historical Vehicle". There is a special filing process for a Historical Vehicle, but I think it is just $25. To be considered a historical vehicle the car needs to be 25 years old or older, and of "historical significance", which nobody at the DMV really questions. The real benefit of getting these plates is that the yearly "tag" registration fee is just a flat-rate of $109/yr (went up from $106/yr last year), rather than being a % of the purchase price. The only side-effect is that Historical Vehicles may only be used for parades, car show events, or other similar specialty activities. All my collectable cars are under Historical Vehicle status, since they are generally driven rarely and I greatly benefit from the low flat-rate.
With Historical Vehicle you will get new license plates, unique to HV status. If you have original/old CA plates that you want to keep then DO NOT surrender them to the DMV, and be sure to keep old registration and Title paperwork with the original plate# on it. As long as you have paperwork showing your car used to have those original plates on it, and as long as you physically have both front/rear plates, then you can later get them reassigned back to your car (meaning to go back from HV plates to your original plates) without too much hassle.
- Wade