I’m looking for an online resource for economic charts, such as for velocity of money. I’d prefer it to be neutral without any statement of economic theory or opinion.
The US Federal Reserve tracks all manner of US economic data: Federal Reserve Economic Data | FRED | St. Louis Fed
The IMF has international data: http://www.imf.org/external/data.htm
I would also recommend the fed chart that Caldazar linked to.
I get the feeling that different people are going to have different opinions as to who is or is not unbiased 
But the fed numbers will often be the source for journalists, such as here:
http://www.washingtonsblog.com/2014/06/velocity-money-u-s-falls-time-record-low.html
Here’s a direct link to the fed’s velocity of money chart:
Okay, that’s just what I was searching for.
Any opinions on why the velocity of money spiked up in the 90’s then gradually tapered off to historically low levels since then? I’ve read that a low velocity of money means that people aren’t spending loosely, but it was falling before the 2009 recession and has been continuing to fall while the stock market rises.
I don’t consider myself to have enough expertise in this area to give a meaningful answer but I think this blog post speaks to your question, although it doesn’t directly address it.
Ed’s blog is pretty good in general, and he’s as knowledgable about economics and money supply as just about anyone out there.
James Rickards writes some interesting thoughts on the velocity of money in his book Currency Wars.