Here's my experience...
Prior to '63, CA DMV allows you to re-assign any plates as long as there clear (no record) in the system. Most DMV employees don't know how to do this. You have to explain that it's a YOM (year of manufacture) plate. For '63 and up, unless the plate came on YOUR car, it can NOT be re-assigned. If you by a car "out of the system" and it has black or blue plates, most DMV employees will tell you that you must get new plates. Not true. If you have any supporting documentation (pink slip, old registration, old insurance card) that shows the original plate number and vin, you can keep the original plates, you just might have to argue some. If you don't have any paperwork, then you can submit the above mentioned form and they'll research the plate.
If you have paperwork with the plate number, there are guys who make "reproduction" plates that are identical to original plates. These plates are also great if your original plates need to be restored (and cheaper, about $200 for a set).
I have also had my late model plates painted black and yellow (looked great on my all black Tahoe), but I'd get pulled over all the time. Never got a ticket ( a lot of cops are car guys), but it wasn't worth the hassle.
The last two options are a HISTORICAL VEHICLE plate or PERSONALIZED plate. I have a personalized plate for my '66, then had my license plate guy re-make them in black and yellow. It's not legal, but on an older vehicle, they normally don't sweat ya. I also don't plan on driving the '66 much anyway. The historical plates are cool, and look better than standard plates and gets people asking questions. A lot of officers don't know how to run them anyway (you have to enter HV as the first letters), so if you paint them or have them remade in blue/yellow or black/yellow, it shouldn't matter much.
Hope this helps. Also, the remanufactured plates and painted plates are technically illegal and for off-road/memorabilia only%)