Nautilus doesn't allow adding/removing bookmarks

Custom bookmarks

To add and remove custom bookmarks, refer to the documentation in Files ▸ Help ▸ Edit folder bookmarks:

Add a bookmark:

1. Open the folder (or location) that you want to bookmark.

2. Click the gear button in the toolbar and pick Bookmark this Location.

Delete a bookmark:

1. Click on Files in the top bar and pick Bookmarks from the app menu.

2. In the Bookmarks window, select the bookmark you wish to delete and click the - button.

The "gear button" is on the right side of Nautilus:

It will be grayed out if the location you've opened is already bookmarked.

Places

The bookmarks seen under the "Places" heading are an exception:

They're not just bookmarks, but XDG user directories with a separate configuration backend, so the Nautilus developers deliberately chose to disable removing them.

The issue of working around this limitation is being discussed in this question.