Ghost is a great blogging platform, but it does not come with a commenting system. If you want comments, you have to embed a third party solution. Platforms like Disqus offer such solutions, however, you give away the data that actually belongs to you and your users.
In addition to data ownage, data availability might become another issue, as various commenting services have been discontinued in the past. One example is Haloscan: Acquired by JS-Kit in 2008, renamed Echo in 2009 when JS-Kit was discontinued. In 2012, it was announced that Echo would discontinue their comment hosting services. Other services may suddenly change their terms and conditions, employ advertisements or disable features such as data export. Think about if and how this might affect you. Losing all your comments or manually migrating hundreds of entries is no fun at all. More pros and cons can be found here.
Fortunately, there are also a couple of open source, self-hosting commenting systems out there, although with varying degrees of maturity. With one of these you'll be in full control at the cost of having more initial setup work to do, caring about hosting, updates, security etc.
The following list of commenting systems, both hosted/self-hosted and commercial/open-source, is in no specific order.
A commenting server similar to Disqus. Comments are written in Markdown, users can edit or delete own comments within 15 minutes by default. Comments in moderation queue are not publicly visible before activation. Isso uses an SQLite backend and offers Disqus and WordPress import. Embed a single JS file of 40Kb (12Kb gzipped) and you are done. Supports Firefox, Safari, Chrome and IE10.
Created for building forums, but also has an interesting comment system: https://blog.vanillaforums.com/news/introducing-vanilla-comments/. Commercial.
With more than 3.5 million publishers using it, Disqus claims to be the leading commenting and community platform on the web.
Facebook Comments Plugin
The comments plugin lets people comment on content on your site using their Facebook account. If people wish to they can share this activity to their friends and friends of friends in News Feed as well. It also contains built-in moderation tools and special social relevance ranking.
An open source commenting system for the blogging platform Ghost. Created with developers at GoInstant, Ouija creates inline comments for blog users and keeps extensibility and theming in mind. A very interesting and elegant approach as you can see in this demonstration:
Discourse is an open source discussion platform built for the next decade of the Internet. It works as a mailing list, a discussion forum and as a long-form chat room. Discourse claims to be "a from-scratch reboot, an attempt to reimagine what a modern Internet discussion platform should be today, in a world of ubiquitous smartphones, tablets, Facebook, and Twitter. [...] Discourse pares all the complexity away and puts just the essential stuff on screen – the conversations you care most about, based on your participation. All the modern amenities you'd expect from a big social website like Twitter or Facebook are present in Discourse. Mention someone by @name. Paste in a link or an image, and we make it awesome on your behalf. Simple quoting and linking of replies and topics. Reply wherever you are, online or via email."
Seriously, this looks good. Not tested though, might be a bit bloated. Requires 1 GB RAM, Docker and a working mail server.
Some Comments aims to be a generic commenting system that can be hosted separately from any page. It works with sites, pages and comments. Also it's single purpose, so it has no authentication of it's own (partly to not have to deal with spam-bots) but offers connections to authentication services like Facebook, Google and OpenId endpoints.
IntenseDebate is a comment system for WordPress, Blogger, Tumblr and other blogging / CMS platforms. Features: threading, email notification, reply by email, commenter profiles, reputation scores, comment voting, comment history, moderation, blacklisting, spam filters, multiple administrators, social commenting (using Facebook, Twitter, Gravatar) and guest commenting without an account.
“When a user submits a comment,” explains Thornton on GitHub, “echochamber.js will save the comment to the user's LocalStorage, so when they return to the page, they can be confident that their voice is being heard, and feel engaged with your very engaging content. It does not make any HTTP requests. Since LocalStorage is only local, you and your database need not be burdened with other people's opinions.” That's right: Once it's submitted, the comment only exists on the commenter's machine. It never reaches your server—or your eyes. The product’s motto brings a tear to your eye: “All of the commenting, none of the comments.”
That said, Hugh Rundle decided to move to Ghost and not have a commenting system at all. Personally, I want to have comments in my blog. But I do like his reasoning about it. You should read it.