LockerService has a (non-exhaustive) list of supported libraries on this post:
Leaflet 0.7.7 and 1.0.2
RxJS Latest as of 12/5/16
jQuery 2.2.2 and 2.2.4
jQuery UI 1.11.4
Other libraries may work, but have not been tested. There will likely always be supported as long as they are secure. Insecure libraries won't work.
Salesforce wants us to be able to use third-party libraries so we don't have to do total rewrites, but they also want data to be secure, so libraries that behave properly will work just fine, and libraries that do not won't be allowed to do things it should not, such as manipulating the DOM outside of the component it is contained in.