These libraries allow you to persist data across browser sessions. Usually they use HTML5 Local Storage and some other tech as fallback.
See Bower search for Store for a list of client-side storage utilities wrapped as a Bower component and which will remain more up-to-date than this list.
Rhaboo - Makes JS objects persistent directly. Just replace occurences of a.b=c with a.write('b',c). Nested objects and array operations supported. Fast because not just stringify/parse. Only relies on localStorage.
AmplifyJS - supports IE 5+, Firefox 2+, Safari 4+, Chrome, Opera 10.5+, iPhone 2+, Android 2+ and provides a consistent API to handle storage cross-browser.
Store.js - supports IE6+, Firefox 2+, Safari 4+, Chrome 4+, Opera 10.5+ and has a consistent, simple API for handling storage on different browsers.
Data.js - Data Manipulation and Graph Persistence for Node.js and the Browser.
Lawnchair - Sorta like a couch except smaller and outside, also, a client side JSON document store. Perfect for webkit mobile apps that need a lightweight, simple and elegant persistence solution.
Artemia - Artemia is a clientside JSON document store like Lawnchair (in the way of CouchDb). It's very very (and very) inspired by Lawnchair (he copy many aspects, normal, i love Lawnchair) but has some specific features (like modules).
PouchDB - Portable implementation of CouchDB
sql.js - SQLite realisation on JS