I don't know the tallest common breed just some exotic ones like the Indian Jamunapari. Nigerian dwarf goats and pygmy are probably tied for smallest. It's somewhat hard to compare since being a meat breed pygmy tend to have the average size figured by weight and being a dairy breed nigerian by height.
According to here http://www.ansc.purdue.edu/goat/factsheet/breeds.htm Saanen, Nubian, and Alpine are all the same size. I would think the meat breeds would be larger but I'm not sure about height. I found the weight on Boer as being up to 300lbs which is more than double either of those 3 dairy breeds weigh.