user145: What data sets exist out there that can be used for engineers to perform statistical analysis against? Hopefully this data is not needing to be scraped, but is available in an importable format or API, though I am open to suggestions on data that APIs need to be written for.  

user153: Mt. Gox trades as Google Fusion Table

https://www.google.com/fusiontables/DataSource?snapid=S364820JWm5

As far as a "wish list", knowing the count, mean, median and average of bitcoin addresses and their "balance" after each block would be useful for knowing over time traction.  By itself it might not reveal all that much to us but it may correlate to other data or indicate a trend that other data doesn't.
An update is done monthly to: 

https://docs.google.com/spreadsheet/ccc?key=0AmcTCtjBoRWUdHJuUE1mUkFxa3A0eHBDQkxZLVVFZmc


user19564: Quandl has many bitcoin data sets.  Here is a collections page of them.  On top of that , it has almost any other time series data you can imagine:  Everything from Stocks, fundamentals to diabetes and fertility rates.  What I love is that there is one easy API to access all of this data, so it is very easy to cross-compare the data sets  There's also an Excel tool if programming is not what interests you.

user61: 
Historic trade data is available from the Bitcoin Charts Market API
Bitcointalk.org forum stats, impression stats for ads, e.g. new member sign-ups per day
Google Trends data for bitcoin. (Can be exported as a CSV file with links at bottom of the page)
Blockexplorer.com stats query page
Blockchain.info API
The Bitcoinstatus.RowIT page has graphs on the number of bitcoin hosts connected, client version and data on hosts/country. Don't see an API but some data is in tables so probably easy enough to scrape.
Chris Moore's answer to this question provides a lot of useful stats. 
Of course the blockchain itself.


145: <p>What data sets exist out there that can be used for engineers to perform statistical analysis against? Hopefully this data is not needing to be scraped, but is available in an importable format or API, though I am open to suggestions on data that APIs need to be written for.  </p>
 153: <p>Mt. Gox trades as Google Fusion Table</p>

<ul>
<li><a href="https://www.google.com/fusiontables/DataSource?snapid=S364820JWm5" rel="nofollow">https://www.google.com/fusiontables/DataSource?snapid=S364820JWm5</a></li>
</ul>

<p>As far as a "wish list", knowing the count, mean, median and average of bitcoin addresses and their "balance" after each block would be useful for knowing over time traction.  By itself it might not reveal all that much to us but it may correlate to other data or indicate a trend that other data doesn't.</p>

<p>An update is done monthly to: </p>

<ul>
<li><a href="https://docs.google.com/spreadsheet/ccc?key=0AmcTCtjBoRWUdHJuUE1mUkFxa3A0eHBDQkxZLVVFZmc" rel="nofollow">https://docs.google.com/spreadsheet/ccc?key=0AmcTCtjBoRWUdHJuUE1mUkFxa3A0eHBDQkxZLVVFZmc</a></li>
</ul>
 19564: <p>Quandl has many bitcoin data sets.  <a href="https://www.quandl.com/c/markets/bitcoin-data" rel="nofollow">Here is a collections page of them</a>.  On top of that , it has almost any other time series data you can imagine:  Everything from Stocks, fundamentals to diabetes and fertility rates.  What I love is that there is one easy API to access all of this data, so it is very easy to cross-compare the data sets  There's also an Excel tool if programming is not what interests you.</p>
 61: <ul>
<li>Historic trade data is available from the <a href="http://bitcoincharts.com/about/markets-api/" rel="nofollow noreferrer">Bitcoin Charts Market API</a></li>
<li><p>Bitcointalk.org <a href="https://bitcointalk.org/index.php?action=stats" rel="nofollow noreferrer">forum stats</a>, <a href="https://bitcointalk.org/adrotate.php?adstats" rel="nofollow noreferrer">impression stats for ads</a>, e.g. new member sign-ups per day</p></li>
<li><p><a href="http://www.google.com/trends/?q=bitcoin" rel="nofollow noreferrer">Google Trends data</a> for bitcoin. (Can be exported as a CSV file with links at bottom of the page)</p></li>
<li><a href="http://blockexplorer.com/q" rel="nofollow noreferrer">Blockexplorer.com</a> stats query page</li>
<li><a href="http://blockchain.info/api" rel="nofollow noreferrer">Blockchain.info</a> API</li>
<li>The <a href="http://bitcoinstatus.rowit.co.uk/" rel="nofollow noreferrer">Bitcoinstatus.RowIT</a> page has graphs on the number of bitcoin hosts connected, client version and data on hosts/country. Don't see an API but some data is in tables so probably easy enough to scrape.</li>
<li>Chris Moore's answer to this <a href="https://bitcoin.stackexchange.com/q/2828/61">question</a> provides a lot of useful stats. </li>
<li>Of course the blockchain itself.</li>
</ul>
