Weather API
Weather API is exactly what is sounds like: a weather API. This API allows developers to include real-time weather for most any location around the world, from airports to small towns and everything in between. It also provides forecasts, historical data, and a lot of other neat little features that may boost the experience for those interested in looking up the weather.
The base cost of the API is $0 (free!), but it does get more expensive if the planned use is on a high-traffic website. Payment plans increase the amount of calls/month, so the more calls expected, the more you need to plan for. That said, small or personal use is free for up to 1 million calls/month.
API Sports
API Sports is an API that allows developers to include all sorts of sports statistics from various sports leagues around the world. This includes, football, basketball, baseball, hockey, soccer, and more. The statistics include team standings and stats, as well as player stats and other interesting stats regarding the league of choice. This API is always free and only requires the user to sign up to their dashboard.
RAWG
RAWG is an API for game information. This includes links to distribution services, information about the game itself, and stats related to the popularity of the game via Steam stats. This API is free and the key comes when you sign up for the website.
Summary
These are just a few among many free APIs that can provide value to any website of any topic. APIs can make development much easier on a developer by providing statistics or other information that may be requried through an API rather than needing to do the research yourself.