You can use Object.keys for that.

const yourObject = {
  "VERSION": "2006-10-27.a",
  "JOBNAME": "EXEC_",
  "JOBHOST": "Test",
  "LSFQUEUE": "45",
  "LSFLIMIT": "2006-10-27",
  "NEWUSER": "3",
  "NEWGROUP": "2",
  "NEWMODUS": "640"
}
const keys = Object.keys(yourObject);
for (let i = 0; i < keys.length; i++) {
  const key = keys[i];
  console.log(key, yourObject[key]);
}

Or Object.entries

const yourObject = {
  "VERSION": "2006-10-27.a",
  "JOBNAME": "EXEC_",
  "JOBHOST": "Test",
  "LSFQUEUE": "45",
  "LSFLIMIT": "2006-10-27",
  "NEWUSER": "3",
  "NEWGROUP": "2",
  "NEWMODUS": "640"
}
const entries = Object.entries(yourObject);
for (let [key,value] of entries) {
  console.log(key, value);
}

Under ECMAScript 5, you can combine Object.keys() and Array.prototype.forEach():

var obj = { first: "John", last: "Doe" };

Object.keys(obj).forEach(function(key) {
    console.log(key, obj[key]);
});

ECMAScript 6 adds for...of:

for (const key of Object.keys(obj)) {
    console.log(key, obj[key]);
}

ECMAScript 8 adds Object.entries() which avoids having to look up each value in the original object:

Object.entries(obj).forEach(
    ([key, value]) => console.log(key, value)
);

You can combine for...of, destructuring, and Object.entries:

for (const [key, value] of Object.entries(obj)) {
    console.log(key, value);
}

Both Object.keys() and Object.entries() iterate properties in the same order as a for...in loop but ignore the prototype chain. Only the object's own enumerable properties are iterated.

My problem was actually a problem of bad planning with the JSON object rather than an actual logic issue. What I ended up doing was organize the object as follows, per a suggestion from user2736012.

{
"dialog":
{
    "trunks":[
    {
        "trunk_id" : "1",
        "message": "This is just a JSON Test"
    },
    {
        "trunk_id" : "2",
        "message": "This is a test of a bit longer text. Hopefully this will at the very least create 3 lines and trigger us to go on to another box. So we can test multi-box functionality, too."
    }
    ]
}
}

At that point, I was able to do a fairly simple for loop based on the total number of objects.

var totalMessages = Object.keys(messages.dialog.trunks).length;

    for ( var i = 0; i < totalMessages; i++)
    {
        console.log("ID: " + messages.dialog.trunks[i].trunk_id + " Message " + messages.dialog.trunks[i].message);
    }

My method for getting totalMessages is not supported in all browsers, though. For my project, it actually doesn't matter, but beware of that if you choose to use something similar to this.

var obj = $.parseJSON(result);
for (var prop in obj) {
    alert(prop + " is " + obj[prop]);
}

Taken from jQuery docs:

var arr = [ "one", "two", "three", "four", "five" ];
var obj = { one:1, two:2, three:3, four:4, five:5 };

jQuery.each(arr, function() {
  $("#" + this).text("My id is " + this + ".");
  return (this != "four"); // will stop running to skip "five"
});

jQuery.each(obj, function(i, val) {
  $("#" + i).append(document.createTextNode(" - " + val));
});