Updating values in a database
Simplifying redundancy
You could do something like iterating over the id attribute of each input element, calling a function to add the handler.
['priority', 'assignedTo', 'vendorticket'].forEach(addChangeHandler);

function addChangeHandler(inputId) {
    $(&quot;#&quot; + inputId).change(function() { //Input/Select tag
        var output = (&quot;#&quot; + inputId + &quot;-result&quot;); 
        var data = {
            column: inputId,
            id: 15
        };
        data[inputId] = $(this).val()
        $.post({
            url: 'includes/view.func.php', // Updating database based on specified row id, column, and value
            data: data,
            success: function(result) {
                $(output).html(result); //Output span either &quot;Saved&quot; or &quot;Save Failed&quot;
            }
        });
    }); 
}

Note the code uses the shortcut method $.post() to allow skipping the request type.
But a simpler technique would be to add a generic change handler that would be called after any change event on any of those inputs. This can be done by combining the selectors passed to the jQuery function:
$('#priority, #assignedTo, #vendorticket')

This can then be used to add a generic function handler that can get the id of the input using .attr('id'):
$('#priority, #assignedTo, #vendorticket').change(changeHandler);
function changeHandler() {
    var inputId = $(this).attr('id');
    var output = (&quot;#&quot; + inputId + &quot;-result&quot;); 
    var data = {
        column: inputId,
        id: 15
    };
    data[inputId] = $(this).val()
    $.post({
        url: 'includes/view.func.php', // Updating database based on specified row id, column, and value
        data: data,
        success: function(result) {
            $(output).html(result); //Output span either &quot;Saved&quot; or &quot;Save Failed&quot;
        }
    }); 
}

If you had a lot more input elements to add to that list, a class could be applied and they could be selected by class name (e.g. $('.inputToWatch')) or else if they were all child elements of a container then a child selector might simplify things (e.g. $('#containerElement input').
Simplifying the success function
The success function could be replaced with a bound function - i.e. a function bound to $(output).html:
success: $().html.bind($(output))

These changes are visible in this phpfiddle.
You could also use the other syntax of $.ajax() i.e. Query.post( url [, data ] [, success ] [, dataType ] )
$.post('includes/view.func.php', data, $().html.bind($(output)));