Views is an incredible module; being implemented into the core of Drupal 8 should be enough, but until them let's explore it for Drupal 7. Views allows a developer to redefine the way content is displayed on their website. Views gives the power to reorganize the position of items in a page or creating new pages to show a different set of data completely. There are many, many more reasons as to why this module is so helpful so head on over to the documentation to get a taste of a few examples.
2. Chaos Tool Suite (Ctools)
Chaos Tool Suite, or Ctools for short is yet another module that will soon be integrated into Drupal 8. With that being said I don't think I need to verify it's validity for helping you create beautiful websites. Ctools allows creating your own custom fields to allowing page management; your experience in Drupal becomes not only easier but greater in simplifing already easy tasks.
Panels allows a developer to reorganize the way a template lays content as well as creating new pages entirely with their own URLs and content given the details you'd like to display.
4. Libraries API
Though this modules does nothing by itself, it will be required by many other modules such as owl carousel, or views slideshow. This module gives language to existing scripts to communicate how they should function.
5. Administration Menu
Drupal already comes with an administration toolbar at the top. This is great but the issue with this is that there are no dropdowns for these items and since you have to click on an item and it brings you to an inner page with yet another sub-menu it seems almost annoying to have to keep clicking through to 'remember' where you saw that one item if you aren't that familiar with Drupal yet. Administration menu will allow these top items to drop down and display their inner most items.