This is a more theoretical question. I am about to build a little server in here and want to create an API for it. I am deciding what is better and already ruled out SOAP since that thing is a mess in my opinion. I am left with REST and XML-RPC. I really enjoy XML-RPC, it is really simple to implement and it is regular enough that all clients can use it easily. These days all the cool kids are doing RESTful stuff, sometimes with a JSON payload or XML document or even HTTP POST VARIABLES. I think those guys always reinvent the wheel for each service. I don't see what one could gain by going with REST over using XML-RPC.
So, can someone here provide practical reasons for implementing an API using REST+JSON over just using XML-RPC?
REST vs RPC implementations like XML-RPC is a false dichotomy. You can implement a RESTful interface using XML-RPC (although you probably wouldn't want to). That said, there are a bunch of reasons why you would want to expose resources in a RESTful way using vanilla HTTP instead of rolling your own RPC interface using a technology like XML-RPC:
See this blog post for more info.