Access MongoDB directly via JavaScript
MongoDB natively does not have a fully usable REST interface. You will need either Python based Sleepy Mongoose or Node.js based MongoDB Rest
Please see http://www.mongodb.org/display/DOCS/Http+Interface for more information.
Mongo's inbuilt REST interface is very basic & read only.
If you happen to host your database on MongoLabs, they also expose a REST API. Watch out, it's not secure, as an API key is passed with each request, but your could use it to retrieve public data through Javascript:
https://support.mongolab.com/entries/20433053-Is-there-a-REST-API-for-MongoDB-
Once you have your mongolab db setup, you can access it thru REST request such as
$.getJSON("https://api.mongolab.com/api/1/databases/your-db/collections/your-collection/?apiKey=your-key", function(json) { //console.log( "JSON Data: " + json );});
Not in the standard security context.
If you have a situation where you have elevated security rights (such as inside a custom browser extension) then it may become possible.