You should use content negotiation for this. The client should have an Accept header that specifies what it wants (which could be "application/json" but really should be something that tells you more about the contents than simply how it can be parsed, such as "application/vnd.mything.MyResource+json" which would be documented in your API with what fields it contains and what it means etc.).
You should also question whether you really need multiple representations for each resource -- in many cases, it's more trouble than it's worth to automatically generate, say, both JSON and XML responses, since it just divides your attention to creating sensible serializations for your API.
If you expect to have clients which cannot modify the headers of their requests, you can support fallbacks like specifying the Accept header in a query parameter. Putting it in the actual URL though is doing a disservice to fully compatible HTTP clients, though.
But if JSON is so inherent to the resource that content negotiation doesn't even matter, it can be fine to include that in the URL, as you might include descriptive filename extensions like ".png" or ".wav" in a URL.
