In addition, countable nouns (like cars, people, cities, but also including multiples of 100, 1000, etc...) change form depending on how many of them there are (1, 2-4, 5-20, 21-24, 25-30 etc...) Usually these separate forms are phonetically related, but sometimes there is no connection at all. These rules don't come in to play when strictly counting numbers until 200, but is an integral part of what makes it hard to count things in Russian.
There are also wrinkles like the word for 40 (сорок) and 90 (девяносто) that don't fit in the usual tens pattern like 20 (двадцать - two * ten) or 30 (тридцать - three * ten). Any Russian speakers care to explain what's going on with those two?