Make Varnish 3.x handle jsonp requests so that we can cache them (even when jQuery generates random callback function names when using $.getJSON). Inspired by https://gist.github.com/simonw/640331 and adapted for Varnish 3.x.

varnish-jsonp.vcl

#<jsonp>
# We go BACK to varnish to get it to generate an ESI template that
# generates a JSON-P response.
backend jsonp_template_backend {
  .host = "127.0.0.1";
  .port = "80"; # use the port that varnish is listening on
}

# <jsonp>
# How the jsonp_template_backend dispatches to the ESI generating code:
sub vcl_recv {
  if (req.url == "/JSONP-ESI-TEMPLATE") {
    error 760;
  }
}

sub vcl_recv {
  # If URL includes callback=, rewrite to an ESI template
  if (req.url ~ "callback=") {
    set req.http.X-Callback = regsub(
      req.url, ".*[\?&]callback=([\.A-Za-z0-9_]+).*", "\1"
    );
    set req.http.X-ESI-Url = regsub(req.url, "&?callback=[\.A-Za-z0-9_]+", "");
    # Remove a trailing ?
    set req.http.X-ESI-Url = regsub(req.http.X-ESI-Url, "\?$", "");
    # Fix any accidental ?&
    set req.http.X-ESI-Url = regsub(req.http.X-ESI-Url, "\?&", "?");
    # Remove %22 (")
    set req.http.X-ESI-Url = regsub(req.http.X-ESI-Url, "%22", "");
    set req.url = "/JSONP-ESI-TEMPLATE";
    set req.backend = jsonp_template_backend;
    return (pass); # NEVER cache template, since it varies on X-Callback/ESI-Url
  }
}

sub vcl_fetch {
  # X-ESI: 1 from backend triggers ESI processing
  if (beresp.http.X-ESI) {
    remove beresp.http.X-ESI;
    set beresp.do_esi = true;
  }
}

sub vcl_fetch {
  # X-JSONP-Server means we need to clean up the response a bit
  if (beresp.http.X-JSONP-Server) {
    remove beresp.http.X-JSONP-Server;
    remove beresp.http.Via; # Gets added again later on, but a bit less messy
    remove beresp.http.Retry-After;
    set beresp.http.Server = "JSONP-Server";
  }
}

# We're using a custom error here because it's the only way I could find to get # varnish to compose a custom response.
sub vcl_error {
  if (obj.status == 760) {
    set obj.http.Content-Type = "application/javascript; charset=utf8";
    set obj.http.X-ESI = "1";
    set obj.http.X-JSONP-Server = "1";
    set obj.status = 200;
    set obj.response = "OK";
    synthetic {"<esi:include />"} + req.http.X-Callback + {"(<esi:include src="} + req.http.X-ESI-Url + {" />)"};
    return(deliver);
  }
}
# </jsonp>