I think developers can do this for their own apps via iTunes Connect but this doesn't help you if you are looking for stats on other peoples apps.
148Apps also have some aggregate AppStore metrics on their web site that could be useful to you but, again, doesn't really give a low-level breakdown of numbers.
You could also scrape some stats from the RSS feeds generated by the iTunes Store RSS Generator but, again, this just gets currently popular apps rather than actual download numbers.