Disclosure: I am part of lobster.wiwi.hu-berlin.de which providers data for academic research.
NASDAQ's Historical TotalView-ITCH sample file:
On NASDAQ's public ftp you can find sample files of NASDAQ's Historical TotalView-ITCH. The files contain message data and have to be interpreted to get tick-by-tick data. I.e. you need to reconstruct the book.
Limit order book data reconstructed from NASDAQ's Historical TotalView-ITCH:
In LOBSTER data samples you can find reconstructed data for several tickers traded on NASDAQ with book levels of 1,5,10,30,50.
Similar data is available from TradingPhysics.