A buyer's agent is not required in the sale of a property, but it's a good idea to have one. The offer you give in writing is legally binding. You could have an attorney draw up an offer for you, but it'll probably be cheaper to have an agent. Also the seller has agreed to pay their listing agent a commission based on the sale of their property. The listing agent then offers a portion of this commission to the selling agent to help them procure a buyer. This means the seller is most likely paying all or most of the buyers agent's services for you.
As for the question of getting the seller to reduce their price because you don't have an agent, the answer is no. If their property is listed, they have a contract with their listing agent to pay a commission. They'll have to pay that commission regardless if you have an agent or not. The seller cannot reduce the commission either, because as stated before, they are obligated to pay the commission agreed to in writing when they listed it if the property sells.
Having a buyer's agent is highly recommended as they'll do a lot of work for you. They'll set up appointments to see properties for you, write up your offer if you decide to purchase a property, spend their time and gas money driving you or meeting you at possible properties, spend their time going through their local MLS to find homes that fit your criteria, set up appointments with appraisers and inspectors and letting them in the property for you, negotiate the best possible price for a property on your behalf, and many other services depending on your situation. All this is, like I stated earlier, paid for by the seller.