Great answers - just wanted to clarify on a some of the comments. JSON-RPC is quick and easy to consume, but as mentioned resources and parameters are tightly coupled and it tends to rely on verbs (api/deleteUser, api/addUser) using GET/ POST where-as REST provides loosely coupled resources (api/users) that in a HTTP REST API relies on several HTTP methods (GET, POST, PUT, PATCH, DELETE). REST is slightly harder for inexperienced developers to implement, but the style has become fairly common place now and it provides much more flexibility in the long-run (giving your API a longer life).
Along with not having tightly coupled resources, REST also allows you to avoid being committed to a single content-type- this means if your client needs to receive the data in XML, or JSON, or even YAML - if built into your system you could return any of those using the content-type/ accept headers.
This lets you keep your API flexible enough to support new content types OR client requirements.
But what truly separates REST from JSON-RPC is that it follows a series of carefully thought out constraints- ensuring architectural flexibility. These constraints include ensuring that the client and server are able to evolve independently of each other (you can make changes without messing up your client's application), the calls are stateless (state is represented through hypermedia), a uniform interface is provided for interactions, the API is developed on a layered system, and the response is cacheable by the client. There's also an optional constraint for providing code on demand.
However, with all of this said - MOST APIs are not RESTful (according to Fielding) as they do not incorporate hypermedia (embedded hypertext links in the response that help navigate the API). Most APIs you will find out there are REST-like in that they follow most of the concepts of REST, but ignore this constraint. However, more and more APIs are implementing this and it is becoming more of a main-stream practice.
This also gives you some flexibility as hypermedia driven APIs (such as Stormpath) direct the client to the URIs (meaning if something changes, in certain cases you can modify the URI without negative impact), where-as with RPC URIs are required to be static. With RPC, you will also need to extensively document these different URIs and explain how they work in relation to each other.
In general, I would say REST is the way to go if you want to build an extensible, flexible API that will be long-lived. For that reason, I would say it's the route to go 99% of the time.
Good luck,
Mike