Disable Comments Plugin
Disable Comments is a plugin that allows you to remove comments from every post, both new and already published. After you install and activate the plugin, you can navigate to Settings -> Disable Comments. Here you will see a few options. You can either choose to disable comments everywhere (on Posts, Pages, and custom post types) or select which post type you want to remove comments from specifically.
Once you’ve disabled comments, the comment form will be hidden from the bottom of posts, existing comments will no longer be displayed, and pingbacks and trackbacks will be shut off.
Turning off Comments on Individual Posts
If you want to disable comments on just a few posts, you can use WordPress’ Discussion feature. Simply go into the post editor of the post where you want to disable comments, and click the Screen Options tab at the top of the page. Check the “Discussion” box and you will see a new Discussion metabox appear at the bottom of the page.
This metabox has two options, “Allow Comments” and “Allow trackbacks and pingbacks”. Uncheck both of these boxes before you publish a post, and the comment form will be removed.
Some Alternatives to Comments
Fortunately, there are a couple of creative plugins that help you manage your comments, and offer alternative approaches.
Disqus is a third party comment hosting service that allows you to get a bit more out of your comment threads, with a few more options than WordPress offers out of the box. Moderation in Disqus gives you more control, and there is a lot of spam protection built in You can choose to open your comments to guests, or allow users to sign in with Twitter, Facebook, Disqus or WordPress to post. Disqus allows you to moderate comments without having to invest as much time into them.