I have good news and bad news.
The good news is that the type of data you're looking for is generally
available, often at no cost.
The bad news is that there is no central database for the nation that
you can simply download and have as your own.
Instead, there are hundreds of individual systems in states, cities
and counties that contain the relevant information. Services like
zillow make an enormous effort to get the data from each and every
source (and where a service like zillow is lacking coverage, that's
often because they weren't yet able to obtain the data from local
So, if you want to start digging, you can find property tax and
assessment values for major jurisidictions.
Here are a few places to start:
Search Real Property Sales Database
Search Real Property Assessment Database
New York City Department of Finance
Office of the City Register
Automated City Register Information System
Chicago and Cook County:
Cook County Assessor's Office: Property Search
Each jurisdiction is different in terms of how to access data, and
procedures for obtaining a full database. You'll have to contact
individual offices to determine of a full dataset is available, and
what is involved in getting access.
Best of luck,