Static site generators like Jekyll are amazing for producing fast, content-based sites, but what if more functionality is needed? That’s where these third party tools come into play.
Comment System: Disqus
Disqus is a great and easy way to add comments to a blog with sizable traffic.
Gallery/Lightbox Scripts: Photoswipe and Lity
It's fairly common to want to include a gallery or lightbox on a website and content management sites can be especially annoying to use with images. Photoswipe and Lity are awesome and lightweight scripts to integrate in a static site.
Calendar: Tockify
Tockify is an interesting option for embedding a calendar if more functionality is needed over Google Calendar.
Forms: Formspree or Formbucket
For integrating the standard form, Formspree is simple and free. Formbucket is a more advanced option if needed.
Ecommerce: SnipCart
I have not used this yet, but it looks interesting. If I ever needed ecommerce features without the bloat of a platform, I'd give this a shot.
CMS for Developers: Contentful, Siteleaf, Statamic
These are my go-tos over WordPress. Please, anything but WordPress.