Handwritten, unwitnessed wills, called "holographic" wills, are legal in about 25 states. To be valid, a holographic will must be written and signed in the handwriting of the person making the will; in some states it must also be dated. Some states allow you to use a fill-in-the-blanks form if the rest of the will is handwritten and the will is properly dated and signed.
A holographic will is better than nothing if it's valid in your state. But a will signed in front of witnesses is better. If a holographic will goes before a probate court, the court may be unusually strict when examining it to be sure it's legitimate. And if you don't have guidance -- from a good self-help resource or a good lawyer -- it's easy to write something that turns out to be ambiguous or even contrary to what you intended.
For information on making a valid but simple will, see The Simple Will: No Frills, No Fuss, No Anxiety.