Core

Entity reference

Refer to other entities (users, nodes, etc.) as a field in an entity. Very powerful, especially when combined with Views.

Libraries

Useful API for third-party PHP libraries.

References

The Drupal 7 version of the user reference and node reference CCK fields. Sadly currently has limited maintenance, and probably replaced by Entity reference module now.

Rules

An extremely powerful module, that many others can work with. Rules allows you to trigger actions based on events and conditions. Events might be "comment added" or "content updated", actions can be almost anything from changing other settings to displaying messages to sending emails, conditions can check values or dates or other things to say whether or not the actions should fire.

Rules allows you to "program" a Drupal website without writing any code.

Site Verification

An essential module if you want to add your site to Google or Bing's webmaster tools.

Token

Most of the Drupal 6 Token module found its way into core for Drupal 7, but this module provides some missing tokens and UI features. This module is still a pretty-much essential module for any site that needs token replacement in text, such as for URL path generation, or "mail merge" email sending.

Views

Yup, this module is extremely useful, and is used on all my Drupal sites. There's a movement to include Views into Drupal Core, just like CCK has become fields in core.

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