Is historical information on the counts of trades in single stocks, futures, options etc. available somewhere for download or purchase? If not, which ways can you think of to gather it?

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Interactive Brokers provides it as a field called count.

In this page of the IB API Reference Guide count is described as follows

When TRADES historical data is returned, represents the number of trades that occurred during the time period the bar covers.

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Ok, so IB provides this data. Nice. This is not an option if you do not trade via IB, but for me and, I believe, many others this is ok. –  Konsta Sep 23 '12 at 12:41
You asked if the data was "available somewhere for download or purchase." You don't have to make any trades in order to get the data although you may have to pay something like 10 or 20 dollars a month. You may even be able to get the data with a paper trading account for free. –  user508 Sep 23 '12 at 14:50
I am undecided which answer to accept. Since I believe that IB offers a lot of asset classes and exchanges and the count is supposedly then available for all history, I opt for this one. –  Konsta Sep 24 '12 at 22:40

Its not available for free anywhere that I know of. Your only option is to purchase tick data for the instruments you're interested in and then count the ticks per trading session (or whichever timeframe you want to use).

EDIT: This link might be interesting for you regarding how to get market data.