This document explains how to delete bookmarks in Safari that is running on Mac OS 10.10, but the same method can be applied for 10.9.
You can quickly delete links from the favorite bar by right clicking and then clicking Delete.
The Bookmarks bar and Bookmarks menu can't be deleted.
Address Book / Contacts (if present) and Bonjour can't be deleted, but you can remove them from the list by unselecting them in Bookmark preferences (found by opening the Safari menu and selecting Preferences... > Bookmarks).
History and All RSS Feeds can't be deleted, but you can delete individual bookmarks within them.