In the backend, a new language for a new service would likely be ok, if it's pretty small.
If you chose any of the major frameworks for your application you'll be good. Django, Rails, Java EE, Spring, Play Framework, Meteor. These aren't likely to go away anytime soon, and they've been around for a while.
On the front end it's a much more dangerous approach. If you have one or two pages that use the latest flavor of the month, Backbone(2011) Knockout(2012), Angular(2013), React(2015), you'll be ok.
The problem comes when you just re write your entire front end app in one of these. I like to experiment with front end technologies on one page, but I would never buy into the SPA for the entire app. The shelf life is way to small. They'll still be supported probably.
If your trying to keep or hire developers, putting backbone.js as a tech you use probably won't get as many applicants as say React.js. Since most front end devs right now are trying to introduce React into current job or jump to a job where they use it.