Could be useful for a browser app which handles 'large' datasets, or for a mobile/desktop app as an SQLite replacement. Think of a messaging app which lets you search conversations client side with decent performance. It has a small footprint and some interesting features, so it might be a convenient DB for some apps even without strong performance requirements.

Cordova is a big one. The ability to have rich queries into some persistent data set is something that's difficult to achieve atm.

Well, it could be very useful as a more advanced "model" layer in browser-side MVC apps. I'm currently working on something that has a pretty complex data structure and simple JS objects/arrays simply don't cut it. LokiJS certainly seems worth looking into.

The feature that looks especially promising is the ability to create Dynamic Views and to listen on notifications on these views.

You can also use them in the browser to cache data to reduce server calls or improve client UI performance (a la meteor.js).