We initially tried it, on a different project, as part of a freemium package with Acquia. It is a GREAT tool to monitor your site and if you take the time to set it up more fully, it can monitor a myriad of key aspects of your site. You can find delays, trends or solve performance problems. It can be a great tool while working on projects, or to build a base line of what your site normally is.
In our use of it, it had some overlap with our own existing internal tools, so we don't use it for normal daily use/ monitoring but it did inspire us to expand our in house tools to create new relevant webstats to show average response times per-site and giving an idea of per-server performance.
Going forward if we need to x-ray a site and normal checks on a site don't fit the bill, using New Relic is definitely a great option.
All hail to New Relic 🙂