This app uses the Open Weather Map (http://openweathermap.org/API) to display weather conditions and forecast in selected world cities. You can search and add your own locations (the data is collected from over 40000 weather stations around the world).
Two kinds of weather forecast are available: 16-day daily weather forecast, and three-hourly forecast for up to 5 days.
This app is free, advert/IAP-free, and open source. The source code is available at
https://github.com/Kestutis-Z/World-Weather.