A little bird just informed me of a Mathematica solution to this question (the underlying implementation still uses JLink, but this answer hides all the java related code):
imgur[expr_] := Module[
{url, key, image, data, xml, imgurUrl},
url = "http://api.imgur.com/2/upload";
key = "c07bc3fb59ef878d5e23a0c4972fbb29";
image = Fold[ExportString, expr, {"PNG", "Base64"}];
xml = Import[url,
"XML", "RequestMethod" -> "POST",
"RequestParameters" -> {"key" -> key, "image" -> image}];
imgurUrl = Cases[xml, XMLElement["original", {}, {string_}] :> string,
Infinity][[1]];
"![Mathematica graphic](" <> imgurUrl <> ")"
]
This is V8 only and the XML import options "RequestMethod" and "RequestParameters" are undocumented and experimental (and therefore subject to change).