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.
Clearly it is a pragmatic trade-off and is popular (Google and Twitter do it). The correct answer will be arrived at by considering the total architecture of your application.
"The Accept request-header can be used to specify certain media types which are acceptable for the response."
Similar to how when you access some linked data URLs you can specify rdf/xml or rdf/n3 in the Accept header to receive the same data in a specific format.
It's not used to specify whether you want a picture of someone or their contact information all from the same URL.