Available on: Gold, Platinum plans
You can use AJAX to submit your forms — this even works cross-origin. Create a new form in your Gold Account dashboard and set the Accept header to application/json.
Here's an example, using jQuery. Note the dataType: "json" property, it's required to set the Accept header.
$.ajax({
url: "https://formspree.io/FORM_ID",
method: "POST",
data: {message: "hello!"},
dataType: "json"
});