I think it is worth it to know your body fat. Although it is scary to ever be placed in a category (i.e. healthy, fat, obese etc..), it is important to have data to reference as you grow older and significant events happen in your life. Although most people who lose weight, and are successful with various dietary changes, they do not consider whether their body fat percentage lowered in the process. The trick is to lose weight because you have lowered your body fat percentage and gained muscle.
There are a few things to look at: 1. your BMI - (BODY MASS INDEX). This is a calculation that uses your height and weight to determine your overall category. 2. your Body Fat - This can be quickly done with calipers or a bio-impedance machine. They both have large margin of error. 3. your Circumferences - This is a measurement made in inches of you biceps, thigh, waist line, hips and chest.
These numbers help you understand how various changes you make in your life will effect your body.