Services
Search
You don't need your own server to have search functionality, as there are services that do it all through APIs.

Algolia
Put all your searchable data in Algolia, and you and query and get results through APIs incredibly fast.

CloudSh Search
Powerful search for your website with a few lines of JavaScript. Works great with static sites!
Elastic Site Search
Provides the tools you need to build a powerful website search.

Google Custom Search Engine
You create mini search engines that are scoped by URL and can then embed them onto your own site.