This is a controversial topic only because there's so much agenda-driven noise around this question.  There are a lot of groups and individuals out there (and we've all run across some of them) who believe that ADD/ADHD is (you pick) 1) the result of bad parenting, 2) a manifestation of low self-esteem, 3) an excuse by lazy teachers, and/or 4) a conspiracy by the doctors and/or pharmaceutical industry.

Sure, bad parenting may contribute to the symptoms, and lazy teachers might increase the number of misdiagnosed kids (since statements/evaluations from those in contact with children are weighted along with other instruments in arriving at a diagnosis), but at its root, ADD/ADHD is a legitimate disorder with a biological basis. 

My background is biology, so rather than dealing with the soft science of psychology or indirect assessments via the field of education (and special education in particular), I'll stick to the lines of evidence for the existence of (and even causal and/or mechanistic candidates for) ADD/ADHD that originate in neuroscience research.  The question of whether ADD/ADHD exists has already been answered by neuroscience, and thus more ambiguous results in other, more subjective disciplines should be interpretted based on what is found there.

A few areas that come to mind in include:

1) Genetics - Families show patterns of heritability.  Taken alone, this only raises the nature/nurture debate; however, specific genes (e.g., variants of certain dopamine receptors) have been isolated that have been correlated with the existence of alcoholism, drug addiction, OCD, and ADD/ADHD.  These additional disorders are, of course, known to be correlated with (i.e., are often co-morbid with) ADD/ADHD.

2) fMRI (function magnetic resonance imaging) - This method shows which parts of the brain are active from moment to moment while performing a given task.  In patients with ADD/ADHD, the prefrontal cortex has been shown to be less active.  This area is thought to be largely involved with impulse control, and in those patients where this structure has been damaged, these individuals are prone to emotional outbursts, acting on short-term impulses rather than acting on long-term planning.  Further, the prefrontal cortex is one of the least mature parts of the brain in children, thus a deficit in that area in an adult often leads child-like impulsivity... which is a characteristic trait of ADD/ADHD.

3) The pharmacological paradox - When ADD/ADHD children are given drugs known to treat the condition (e.g., stimulants), their hyperactive and/or attention deficient symptoms tend to dissipate in a dose-dependent manner.  By contrast, "normal" children tend to become more active and less focused when given the same medication.  Essentially, this points to the existence of two separate populations, one of which, obviously, is composed of children with this cluster of symptoms we have identified as ADD/ADHD.

4) Additional causal hypotheses - In addition to being a heritable trait, instances of ADD/ADHD (or symptoms thereof) are correlated with a history of childhood illness and/or trauma.

One of the problems that critics of the verifiability of ADD/ADHD point to is the subjectivity of psychological tests.  Specifically, diagnoses are made from questionnaires on which patients self-report their symptoms and from external assessments from parents and teachers that are arguably even further removed.  The areas highlighted above are less subjective and, taken together, make a stronger case for the existence of a genuine medical condition.  That is something that needs to be communicated to the general public who might otherwise be swayed by groups who have a stake in refuting this diagnosis and/or the existence of this disorder.  That being said, input from the realm of psychology continues to validate the diagnosis and offer suggestions for treatment as well as assays to evaluate treatments based both in psycho-social realm and pharmacological in nature..