By default commenting is enabled on both Posts and Pages in WordPress. Here’s how to disable it:

Existing Posts

1. Click Posts in the left navigation.
2. Click the checkbox in the section header (to the left of Title) to select all pages.
3. Select Edit from the Bulk Actions dropdown and click the Apply button.
4. Select Do Not Allow from the dropdown to the right of Comments, then click Update.

Existing Pages

Same as above, except click Pages in Step #1.

Future Posts & Pages

1. Click Settings >> Discussion in the left navigation.
2. Uncheck the checkbox next to Allow people to post comments on new articles.
3. Click Save Changes.

You can also disable / enable comments on individual posts or pages by clicking the Quick Edit link then (un)checking the Allow Comments checkbox.

This checkbox is hidden by default on the page / post edit page. To show it by default (allowing you to enable / disable commenting on an individual page / post basis), click Screen Options then check the Discussion checkbox.