Most of the standard functionality of Drupal is actually written as a module. There are several that are disabled by default, but which could come in really handy for many types of websites such as:
features)The Features is strictly for developers. It allows you to convert database objects (views, content types, etc.) into a module. Because a module is a collection of files, it can be version controlled (say, in GIT). If you make an update to a featured object on your local instance, and then push it to a Dev server, the Dev server will recognize that a change has been made and you can then apply the update.
devel)Gives you the ability to send debug messages to the screen. More information here...
https://drupal.org/project/search_krumo
This is used in conjunction with Devel for debugging your pages.
ctools)This is required by the Views module.
views)Just gotta have it, man.
admin_views)Provides a better interface for system admins to look at content (.../admin/content) and people (.../admin/people).
advanced_help)The Views module uses, but does not require, this module. It allows you to store your help file in pure HTML files — awesome for custom modules.
link)A very popular module that provides a standard custom content type for hyperlinks. This became part of Core in Drupal 8.
module_filter)For administrators, this allows you to group, filter, and find your modules quickly