Yes, you can write your own will. This type of will is called a HOLOGRAPHIC WILL. What exactly does that mean? You can prepare this Will anywhere. The only requirements are that it is wholly in your handwriting, it is signed by you, and it is dated. It can be written on anything! A piece of paper, the back of a menu, the back of a business card, and the list can go on.
These Wills must have testamentary intent. What does this mean? I suggest you have the words Last Will and Testament on the top of the paper. Although this is not absolutely necessary, it is recommended. It should revoke all previous Wills and Codicils signed by you. It should also fully dispose of all of your property and not just certain items. It should appoint an Independent Executor to serve without bond and without court supervision. (Hint: these are buzz words we recommend). Another word of caution I would give is that although this Holographic Will is completely valid, it is not recommended to be used in every situation.