Uninstalled and removed the visitors module => reduced the database size by 20GB.
Reduced the access log to only hold 3 days => reduced the database size by 800MB.
Unistalled the Apache Solr modules which were not used any longer and removed the according tables.
Deleted the views data export module which was defectiv.
Deleted the outdated and no longer supported module imageapi
Installed the module module_missing_message_fixer to get rid of error messages regarding not properly removed modules (most likely relikts from Drupal 6).
Removed the migration tables from the database, which are no longer required but haven't been cleaned after the migration from Drupal 6 to Drupal 7.
Security Updates:
Drupal 7.59 => 7.67
Context 7.x-3.7 => 7.x-3.10
Easy Breadcrumb 7.x-2.15 => 7.x-2.17
Lightbox2 7.x-1.0-beta1 => 7.x-1.0-beta2
Link 7.x-1.4 => 7.x-1.7
Mime Mail 7.x-1.0 => 7.x-1.1
Module filter 7.x-2.1 => 7.x-2.2
Universally Unique ID 7.x-1.2 => 7.x-1.3
Views 7.x-3.20 => 7.x-3.23
XML sitemap 7.x-2.3 => 7.x-2.6
The Glossify module is no longer supported for Drupal 7, there is however a version for Drupal 8. We keep the module for the time being.