Dojo 1.6 introduces a new data store API called Dojo Object Store. This new store API is based on the HTML5 IndexedDB object store API and is designed to greatly simplify and ease the interaction and construction of Dojo stores.
Update: dstore is developing as a successor to Dojo object stores, so if you are starting a new application, you may want to look into this project. However, this blog post still describes an important API that is widely used, and is foundational for dstore, sharing much of the same philosophy and even much of the interface.
Dojo 1.10 also includes new stores in dojox/store for local database support. Check the latest blog posts for more information about this.