Can I buy a house without an agent, and demand the 2-3% commission promised to sellng agent for myself?<br/>I'm specifically asking about California if it makes a difference

The agent gets the commission from the seller's amount, not from the buyer. Without an agent, you would simply not have to pay anyone 2-3% commission, but think of what you would lose out on by not having an agent.

Real estate agents:
1) have a thorough knowledge of the real estate market in their communities.
2) know which neighborhoods will best fit clients' needs and budgets.
3) are familiar with local zoning and tax laws.
4) know where to obtain financing for the purchase of property.
5) arrange for title searches to verify ownership.
6) arrange for meetings between buyers and sellers during which they agree to the details of the transactions. In a final meeting, the new owners take possession of the property. 7) act as intermediaries in price negotiations between buyers and sellers.
8) may help to arrange financing from a lender for the prospective buyer, which may make the difference between success and failure in closing a sale.

I have bought and sold homes for 30 years and would never do it without a buyers agent.

But no, you can not ask for a commission since you are not a licensed agent, it is illegal to pay commission to anyone without a current license,

If this is a FSBO, you may ask for a price reduction equaling the 3%. That if fairly common. Actually better since a commission is considered income and you would have to report it as income.

"without an agent" without which agent, yours or the sellers? Like Chick points out, no on the commission but you can bid any price you want.

If the seller has a agent and it is a listed property, then the full commission is paid as per the listing contract. A non licensed person can not get part of that commission.

You may always ask as terms of your offer, for a lower price, even that the selling agent accept a lower commission, they most likely will not accept, but you can make any term part of your offer if you want, as long as it is legal.