First off, it is not illegal to transfer certain guns without paperwork in California. However, it is vitally important to be sure, prior to the transfer, that the gun you are considering transferring is in fact legal to do this with.
Assumptions Made in This Guide
It is assumed that you may legally own firearms in California. I normally assume that the reader realizes this, but this sort of topic tends to attract folks who think there's "a way around" that non-pardoned/non-expunged felony conviction active on their record. While they may manage to get a gun, it is still illegal for them to possess it.
Antique or Black Powder Firearms
Guns made before (but not including) 1899, including handguns, are legally not firearms unless they are loaded. They may be transferred legally without paper, cash and carry. Black powder firearms, including modern designs, are also considered non-firearms.
Long Guns Over 50 Years Old
Rifles and shotguns over 50 years old may be transferred legally face to face, from another person. They may not be bought from a store without paperwork! Handguns may not be tranferred without going through a PPT or DROS process. It is worth noting that a C&R holder must log all C&R firearms they acquire or dispose of, so if you are a C&R holder or are purchasing from a C&R holder, this is not truly a paperless transaction. There simply aren't any 4473 forms involved.
Building Your Own Receiver
It is legal to finish your own receiver in California. However, you must be the one building the receiver, not some friend! At present, the most popular means of doing this is with AK-47 flats, although some folks are doing G3 or AR-15 receivers as well. When building your own receiver, you may complete it as either a rifle or pistol. However, it may be advisable to stamp the receiver with something to alleviate law enforcement concern, such as your own name and the words "NOT FOR TRANSFER". A completely unmarked weapon, with no serial number or other identifying marks, will tend to leave LEOs wondering if you actually built the gun you say you built. In the case of home-built handguns, you are not required to send in a handgun registration form. However, bear in mind that if you were to be caught carrying it concealed without a concealed weapons permit, you are ineligible for the first-offense infraction penalty, and will go straight to felony territory.
Regardless of the age of the gun, a parent or grandparent may give a gun to (or receive a gun from) a child/grandchild without going through the DROS or PPT process, provided that both giver and receiver are California residents. The last part is absolutely insurmountable here - if one party lives outside of the state, the transfer must go through a licensed firearms dealer.
In the case of long guns (rifles or shotguns), there is no paperwork requirement and it is entirely legal, provided the recipient is 18 or older. It is absolutely not legal to give a long gun to a sibling, cousin, etc. There is, however, nothing to prevent a child from giving a gun to a mutual parent or grandparent, who then gives it to his sibling.
In the case of handguns, the child is required to submit an Intra-Familiar Transfer Form, along with a $19 check, to the Department of Justice in order to register the transfer. In the case of handguns, the child must also possess a valid HSC (Handgun Safety Card). Although it is illegal for a dealer to sell a handgun to someone under the age of 21, it is not illegal to administer the HSC test (however, it can be difficult convincing an FFL that it's legal!) in order for him/her to legally register a intra-familiarly transferred handgun. However, this is certainly not a paperless or unregistered transfer.
-- SeanNewton - 01 Nov 2007