A weird issues came up after upgrading from Views version 7.x-3.7 to 7.x-3.8. The pager was missing from all views.
After making sure that there are enough results to bring up a pager, and that the pager ID was unique for each view that shows up in the same page, we noticed the one thing that all views had in common: They all used Global: PHP fields.

It seems that this is a known issue and that there is a patch that people confirm it works.
More info about this issue is available here: https://www.drupal.org/node/2276165
and the working patch for Views PHP module v1.x is here: https://www.drupal.org/files/issues/views_php-search_api-paging-2123315-...

Pager showed up just fine, after applying this patch.