This would be a really useful feature - save a bit of time in following up on comments. I don't think it would actually be that hard to implement, as everybody already says, the data is already saved and freely available.
That said, here's a userscript to show the number of comment upvotes.
It adds a button next to each comment listing to show the score of it. I purposely haven't made it automatic because it would send way too many API requests in a short time and will probably cause you to get throttle violations every time you went on your profile!
It works for your comments (all actions
tab > comments
) and any responses (responses
tab).

// ==UserScript==
// @name Show comment scores
// @namespace http://stackexchange.com/users/4337810
// @version 1.0
// @description Shows your comment and comment reply scores in your profile page
// @author ᔕᖺᘎᕊ (http://stackexchange.com/users/4337810)
// @match *://*.stackexchange.com/*
// @match *://*.stackoverflow.com/*
// @match *://*.superuser.com/*
// @match *://*.serverfault.com/*
// @match *://*.askubuntu.com/*
// @match *://*.stackapps.com/*
// @match *://*.mathoverflow.net/*
// @grant none
// ==/UserScript==
setTimeout(function() {
var sitename = $(location).attr('hostname').split('.')[0];
$('.history-table td b a').each(function() {
id = $(this).attr('href').split('#')[1].split('_')[0].replace('comment', '');
$(this).after("<span class='showCommentScore' id='"+id+"'> show comment score</span>");
});
$('.showCommentScore').css('cursor', 'pointer').on('click', function() {
that = $(this);
$.getJSON("https://api.stackexchange.com/2.2/comments/" + that.attr('id') + "?order=desc&sort=creation&site=" + sitename, function(json) {
that.html(" " + json.items[0].score);
});
});
}, 500);
This will be in the next version of my SE Optional Features userscript, and you can grab the development version (with this feature in it) over here.