It goes without saying that the way your website looks is very important, but how about how it is performing? Do you keep up with the "little" things that may be missed? By skipping these "little" things you can seriously affect your website in a bad bad way.
Google Webmaster Tools is a must have for anyone who has a website.
Google Webmaster Tools is a free tool from Google that you use on your site to monitor things like search queries, sitemaps, Google's access to robots.txt, and most importantly monitor 404 links on your site.
In Webmaster Tools you can submit a dynamic sitemap built by your CMS (or plugin to your CMS). By submitting your sitemap to Google you are telling it each and every page that is on your site. This allows Google to discover your full site faster than finding it while crawling the web.
As your site changes and grows the dynamic sitemap will update Google that there is new or updated content. Google says in every help doc about sitemaps that they do not guarantee that they will index every page, but still having a sitemap is the best method to ensure that search engines learn about your site and its content.
A cool feature of Webmaster Tools is the HTML Improvement section. Here, Webmaster Tools will tell you if you have duplicate meta descriptions, meta descriptions that are too long or short and issues with title tags.
Those are all important to be in good standing because Google may rank your site lower if you are a big offender.
In Webmaster Tools one of the biggest things you want to look for are 404 errors. 404 errors on your site are killers. They look bad to your customers who land on them, even the really good ones. Even worse, they destroy any SEO ranking that you've built up over the years. Not cool, Robert Frost.
Looks like I have 33 404 errors on my site (I'm only showing the first 3 here). What that means is that since the last time I checked people have clicked on 33 dead links. I need to get those fixed as soon as possible.
Right on this Site Errors page I can download the report to a spreadsheet or Google doc to instruct my CMS to redirect the dead URL to a new URL of my chooising with 301 redirects.
How you need to format the old and new URLs all depends on the CMS or plugin that you're using. Here's a handy guide if you're on HubSpot.
Webmaster Tools is a great service from Google which also offers many other tools that you or your webmaster should review at least once a month.
Bing also offers webmaster tools, so make sure that you are set up there, too.