Contentful and Prismic are ones I'm familiar with and they actually support both static generation and API-driven so you can take an incremental approach.
I use forestry+Jekyll on all my own sites and it works great. It's fun to see how far it's possible to go with it.
However I'm still waiting for the right client project to come along to use it with as it's rare for someone to need a custom-built site and also the fairly limited features of a static cms.
Usually if they want a simple site something like Squarespace will be the quickest and cheapest option, whereas if they have any complex requirements, like migrations or integrations with other platforms, then an open source cms framework like Drupal is often a better starting point.
I've used (and paid for) Siteleaf in the past, and Jekyll Admin is really close to it and is OSS if anyone reading is looking for an open/free alternative :)