I presume you are talking about the security or "initial deposit". If you are, read on. If you are asking what downpayment is needed to procure a loan for any particular piece of property, then submit a question specifically about that, and we will be happy to guide you.
Let's start with the contract. The California Residential Purchase Contract (RPA) allows the seller to potentially claim up to 3% of the purchase price for "liquidated damages." That is, if the buyer fails to abide by the terms of the contract, and in doing so "harms" the seller, the most the seller can claim as money damages is 3%. So, as a seller, you might want to see the buyer deposit as much as 3% of the purchase price.
But the buyer is not necessarily well served by offering 3%. Afterall, putting your hands on $15,000 as a deposit on the purchase of a $500,000 home, may not be feasible or prudent. Let's say an unforeseen event takes place on the 27th day of escrow, and you (the buyer) have to bail out of the contract. IF you have to forfeit some money, you want it to be the least amount possible.
Here's an idea, then. If you are well represented, have experience with home buying, and are conversant with the contract, its terms and contingency removals, AND IF YOU WANT TO LOOK GOOD TO THE SELLER, then offer a higher percentage. If, however, you have limited experience with contracts, are worried about your representation, and would't know a contigency if it hit you in the head, then think deposit on the low side.
Of course, experienced Realtors will have submitted many offers, know the approximate amounts of deposits being offered by agents in a particular area, and may be a source of help for you in this. Just remember that YOU, and YOU ALONE decide how much you are willing to risk in an attempt to garner and win any offer. The security deposit is not intended to threaten or punish any party to the contract who acts in good faith, follows the rules of the contract, and is honest. Hope this helps you, Loretta!