In my past experiences running on trails, the paths are demarcated for hikers and bikers and I learned about these running-appropriate paths through word of mouth and in person park information. After moving to New England and the New York area, I haven't been able to discover a definitive resource for finding wooded running trails that include some information and reviews about the path and surrounding area. Does a resource like this exist describing running trails in this area? If not, how do I find running appropriate trails?
I have not seen information regarding trails specifically from a running perspective, but there are a number of sites with information on hiking trails. Most trails suitable for hiking can also be used for trail running, and most trail reviews will cover sketchy sections which will be even more important if you're running.
I am not in New England, so I cannot vouch for the accuracy for any of these sites.
http://www.mountainsummits.com/homepage/mountains.htm/: Information on mountain summits in NE.
Well, depending on your definition of "known" and "documented", you're in luck. There's a workout tracking app that has gained enough popularity in New England to map out a large number of trails. In the areas I can geographically confirm, all the well-traveled trail-running trails have been tracked multiple times using Strava, and hence show up strongly highlighted on their Global Heat Map.
So for a great map of well-traveled trails (many of which do not appear on published maps), check out: http://labs.strava.com/heatmap/#6/-75.12855/42.91677/yellow/run
American Trail Running Association keeps a list for every state. It's not an exhaustive list, but it has some details for running.
Most trails for hiking are also good for running. In fact, I'd make the assumption that a hiking trail is a running trail without specific knowledge that makes it inappropriate.
One way to get a list of trails others deem acceptable for running is to use those that trail races are run on. There are quite a few of those. For example in my area, trail races are held every fall in the Groton Town Forest. The specific routes used are carefully cleaned up over the previous week, but really, these are just ordinary hiking trails that work out to the right distances.
The Groton Town Forest race is part of a larger trail races circuit. You can probably find a list of the other races by digging around a little. All those will show you courses that are obviously fine for running.
However, I know several avid trail runners in town, and they use a number of our local trails that aren't special with respect to running versus hiking.
Local trails will largely be documented on local web sites. Again, you haven't specified your location so I can't tell how relevant it is to you, but if you're near Groton MA, check out http://www.grotontrails.org. We have a network of over 110 miles of trails (more miles of trails than paved roads), and I can't think of good reasons why they aren't just as runnable as they are hikable. And, we're just one town in north-central MA.
For longer routes, check out some of the regional trails, like the Midstate or M&M, in central MA, but there are others in other regions.