You don't 'have' to put an earnest money deposit in with your offer. However, if you want the seller to seriously consider and possibly accept your offer, you should. (Sellers use the earnest money deposit to gauge how serious buyers are with their offer and if they have other offers with earnest money deposits and yours doesn't, they will most likely accept the other offer(s) over yours - assuming all other conditions of the offer(s) are comparable). In CA, the earnest money deposit is usually 1%-2% of the purchase price of the property. The higher the earnest money deposit, the more serious the seller will consider the buyer to be. However, remember if you breach contract, you could loss the earnest money deposit.
Good Luck house hunting!