I first ran across the Net Promoter Score through a post by Eric Ries and it seems like a simple but effective measure of how happy your customers are. Its beauty is how basic it is, which both makes it easy to interpret and straight-forward to gather without annoying your customers.
Unfortunately there don't seem to be any off-the-shelf solutions to help gather the information. In the past I've created surveys through companies like SurveyMonkey, but that's both a pretty intrusive experience and they don't give you any way to calculate an NPS without downloading the raw data into Excel and doing it yourself!
It works by randomly bringing up an in-page popup, asking the user whether they'd recommend the service to a friend, and then requesting any other comments. The data gets passed back to the server and stored in the database, where you can then get a very basic HTML report, or pull the data as JSON to pass into your metrics pipeline, for things like daily email reports.
You can download the code here:
If you want to try in action, here's the demo page:
I'm testing it on my own site but the code is still pretty pre-alpha, so don't be shy with bug-fixes and other modifications.