I've been asked a few times what modules I'm running on the drupal installs I'm tending.

Site #2 is a firewalled company intranet focused heavily around the concept of using organic groups to allow users to post content only to relevant groups. It's running under 6.x, currently 6.8, with comments enabled. (Site #1, my single-user blog domesticat.net, was written up here.)

Modules that are installed but unused because I haven't configured them yet are bolded. Modules that I will turn back on the moment I've got a bugfix are italicized.

I'm undoubtedly missing some fantastic ones, but these are the ones I know about and rely on.  Mind you, sites of this size are going to be far more tailored than, say, a single-user blog, but this list gives you an idea of what it took to create ours.

Commerce and fundraising

civicrm - a huge, comprehensive donor / campaign / fundraising suite of modules. Just barely beginning testing on this module.

ubercart - a comprehensive e-commerce suite.

Connectivity

ldap_integration - LDAP authentication.

Custom content types or content presentation

email - Creates an 'email' field type in CCK.

faq - Creates a 'faq' content type with questions and answers.

insert_view - Allows the ability to insert multiple views (see the Views module under 'Utter basics') into pages to present multiple instances of content lists on a single page

office_hours - Creates an 'office hours' fieldset with open/close times in CCK.

quiz - Creates a 'quiz' content type, with the ability to add questions of several different types to the quiz.

quotes - Creates a 'quotes' content type. We're librarians. We like our words.

signup - Allows users to sign up for events (which are 'event' node types, see 'Dates, calendars, and events)

webform - Creates a 'webform' content type, and lets you populate it with the fields of your choosing, tailor its recipients, and download aggregate results in spreadsheet format

Dates, calendars, and events

birthdays - Provides birthday-related lists and functions.

calendar - Creates a calendar that can be populated with nodes of type 'event.'

date - API to facilitate the usage of dates in several modules

event - Creates a content type 'event' which can be added to calendars or set up for signups

Development-related

admin_menu - Runs a black bar across the top of the admin's screen with shortcuts to common administrative tasks.

coder - helps convert modules from one major version of drupal to another

deadwood - helps convert modules from one major version of drupal to another

devel - Various developer and debugging tools, including dumps of the variables used to create a page.

drush - command line shell for drupal

Image-related

fusioncharts - Allows the creation of flash-based Fusion Charts in nodes.

image - Allows uploading, resizing and viewing of images.

imce - An image/file uploader and browser supporting personal directories and user quota.

img_assist - Insert inline images into posts

jquery_plugin - API for plugging in different jQuery plugins. Required by Slideshow Creator.

slideshow_creator - Creates jquery-based slideshows.

Organic groups

job_queue - Allows jobs to be queued during cron. Useful for OG sites to spread out the load of email notifications.

og - Allows creation of 'organic groups,' which are groups based on interest or content. Sounds simple, but this one module is the core of the entire site.

og_mandatory_group - Requires all new users to join a certain group. For us, ensures that all users monitor the group we use for sitewide news.

URL structure and navigation

custom_breadcrumbs - defines custom breadcrumb trails for content types

pathauto - defines custom URL patterns per content type

token - gives access to custom tokens, like creation date, author, title, etc. for many uses, including defining custom URL patterns

User notifications

messaging - Base module for user-to-user messaging.

notifications - Allows users to subscribe to email notifications on when certain events take place.

User-friendly options

ed_readmore - customizes the "read more" link in posts

fckeditor - WYSIWYG editor

nice_menus - CSS/jQuery drop-down, drop-right and drop-left menus to be placed in blocks

persistent_login - provides a 'remember me' cookie

stringoverrides - Allows overriding and replacement of any string presented to the user from drupal core or any module. Useful if you want to rename basic functions or sections of Drupal.

Utter basics

advanced_help - used to provide extra help in Views

cck - Allows you to define custom content types, instead of being limited to common options such as 'blog post' or 'poll' or 'photo'

contemplate - Content Template allows you to define the layout for your custom content types.

views - Sort, filter, remix, and present whatever content you want in whatever layout and format you want. (Obscenely powerful.)

Not ported to 6.x, boooo

advpoll - Advanced Poll allows you to create several different types of polls. Seems stuck in development hell.

Edit: I should note that I'm quite close to abandoning waiting for advpoll and going with the Decisions module, of which advpoll was a fork.  It looks like it does most of what I want, and has actually been released for 6.x