Disables blinking caret in Google Docs and turns it into pretty blue colour. https://greasyfork.org/cs/scripts/4053-unblinking-blue-caret-in-google-docs

gdocsunblinkcaret.user.js

// ==UserScript==
// @name          Unblinking Blue Caret in Google Docs
// @description   Disables blinking caret (cursor) in Google Docs, makes it a bit thicker and gives it a pleasant blue color, ala iA Writer.
// @id            gdocsunblinkcaret@jnv.gihtub.io
// @namespace     https://jnv.github.io
// @domain        docs.google.com
// @include       http://docs.google.com/*
// @include       https://docs.google.com/*
// @author        Jan Vlnas http://jan.vlnas.cz
// @developer     Dan Burd http://danburd.com
// @version       2015.7.12
// @grant         GM_addStyle
// @downloadURL   https://gist.github.com/jnv/f9dac5f5ff24fc843bf0/raw/gdocsunblinkcaret.user.js
// @icon          https://gist.github.com/jnv/f9dac5f5ff24fc843bf0/raw/icon.png
// @screenshot    https://gist.github.com/jnv/f9dac5f5ff24fc843bf0/raw/screenshot.png
// @license       CC0 1.0; https://creativecommons.org/publicdomain/zero/1.0/
// ==/UserScript==

var myCaretSel = '.kix-cursor-caret[style*="rgb(0, 0, 0)"]';

var style = '.docs-text-ui-cursor-blink { animation: none !important; }' +
            myCaretSel +' { border-color: #0bf !important; border-width: 1px 0 1px 3px; border-style: solid; }';
GM_addStyle(style);

icon.png

screenshot.png