I needed to implement a "trim" on whatever was pasted (remove all leading and trailing whitespace) while still allowing the use of the spacebar.
For Ctrl+V, Shift+Insert and mouse right-click Paste, here is what I found worked in FF, IE11 and Chrome as of 2017-04-22:
$(document).ready(function() {
    var lastKeyCode = 0;
    $('input[type="text"]').bind('keydown', function(e) {
        lastKeyCode = e.keyCode;
    });
    // Bind on the input having changed.  As long as the previous character
    // was not a space, BS or Del, trim the input.
    $('input[type="text"]').bind('input', function(e) {
        if(lastKeyCode != 32 && lastKeyCode != 8 && lastKeyCode != 46) {
            $(this).val($(this).val().replace(/^\s+|\s+$/g, ''));
        }
    });
});
Two caveats:
- If there is already text when the paste occurs, trimming occurs on the entire result, not just what it being pasted. 
- If the user types space or BS or Del and then pastes, trimming will not occur.