My difficult child's tested things like memory, executive functioning, motor-visual abilities...
Actual tests were called Bender Visual-Motor Gestalt Test, Delis-Kaplan Executive Functioning System, Halstead Reitan Test Battery, Rey Complex Figure Test, TOVA Visual Continuous Performance Test, Wechsler Intelligence Scales for Children (WISC-IV), Wechsler Individual Achievement Test WIAT-II), Wide Range Assessment of Learning and Memory (WRAML-2), and assessment of several different parent, teacher, and self-reporting forms. Like Smallworld pointed out though, I think these can vary depending on age and specific areas of concern. It's my understanding that psychologists, specially trained in neuropsychologist. testing, need to be the ones to administer these, but I'm not sure how much of a requirement that is.
It was our experience that these tests were helpful, especially with IEP issues, but not helpful in diagnosis because difficult child has a mood disorder and the psychiatric difficult child had apparently isn't in to diagnosis'ing those. The psychiatrist was most helpful (broad-minded) in that area- but again, in my humble opinion, that's largely dependent on who you have and what the specific areas of concern are.