If you are new to drupal, then this list is for you. These are some of the best of the best drupal modules. Everything from standard framework modules, to location and mapping is covered. Note that if you've been emersed in drupal for some time, than this will be "old news".
The Big Three
"The big three" are important enough that they deserve a category of their own. Most drupal modules worth using have integrated with one of these three. Their importance simply can't be stressed enough.
Content Construction Kit (CCK) - Part of drupal 7; still a contrib in drupal 6. Allows you to define new content types (e.g. blog entry, event, or employee record...) and add "fields" to them. A field could be plain text, an image, a flash video, or whatever. You can also adjust how these fields display in the live view. No drupal install should be without this module.
Views - Broadly speaking, this module empowers non programmers to build dynamic streams of content displaying any number of fields. The content may come from nodes (a.k.a. content types and fields), users, system log entries, etc. You can display this stream in any number of formats including RSS feeds, tables, or just the vanilla view for a content type. You can also create pages or blocks -- its very tightly interwoven with drupal. Nearly every drupal module worth using is integrated with this module. Extremely powerful when used in combination with CCK.
I believe Panels + CCK & Views is a hint at what drupal will look like 3 years into the future. I had to change my pants after the first time I witnessed it. At a very simple level, you could think of it as a layout manager. Create a 1,2,3 column layout. Or a 3 column layout with a full width footer and header, and plop pieces of content in them -- say a view, a block, or a node. That description, however does not do it justice. Since version 3, its positioned itself as a replacement for drupal core's clunky block system. It can now override a node page, and can be used to place content all over the place. It also introduced a concept of contexts, selections rules, and relationships. These are concepts that deserve a series of blog posts, but lets just say its solving some of the weirdest, mind numbing, bug creating problems found in advanced websites. Ironically, I used to hate this module, but after version 3 I will defend its awesomeness to the death!