How do you decide which patients need braces for their teeth?

Diagnostic criteria. "need" is a relative term, because nobody ever died from not implementing orthodontic treatment. The intent is to optimize the "occlusion"-- the way the teeth are spatially arranged. The occlusion is compared to what is by convention considered to be an ideal bite; this comparison is done my means of visual examination and skull x-rays. Severe divergence from this ideal calls for treatment.
Elective. Patients choose to have orthodontics: it is an agreement between the orthodontist and the patient. If their is sufficient malocclusion that i feel a patient will benefit from and the patient desires to undergo such treatment: we begin. If an orthodontist is extremely busy, they must prioritize which patients will be best served and then "go down the list".
Need or want? Do you have symptoms such as tmjd or impacted teeth? Very few people really "need" braces. No one ever died from crooked teeth. However, there are some extreme cases in which the patient would benefit greatly from braces. Get an evaluation from your orthodontist to determine your "need" for braces. It's really up to you and your orthodontist as to whether you really need them or want them.
Normal v abnormal. Teeth and jaws were are designed to meet and function in a specific manner. Variation from the norm indicates need for corrective rx. The better teeth and jaws are aligned, the better they work, the easier they are to care for, the longer they last, the less expensive their maintenance. See an orthodontic specialist for an individualized review of your personal need.
Many factors. There are numerous factors in determing need for braces...Crooked teeth, occlusal discrepancies (bite is "off"), skeletal issues (one jaw larger/smaller than other), positioning of jaws in relation to each other, and more. Cosmetic/esthetics is also another reason to have braces, although it may/may not be a necessity. Have a consultation with doc and discuss issues.