I have an electric water pump, which I want to control over the internet. Currently I know that smart plugs can be used but this requires me to be in the same WiFi network. Are there any smart plugs or ready made solutions where I can control the power switch remotely?
Some smart plugs can be controlled over the internet without having to be on the same network. D-Link Smart Plugs (http://us.dlink.com/products/connected-home/wi-fi-smart-plug/), for example, have a linked app that allows you to switch the plug on and off from anywhere as well as setting schedules. They can also be connected to things like the IFTTT system https://ifttt.com/ for more sophisticated control.
The Belkin WeMo sockets can also be controlled remotely from the app.
Basically any socket with support for Alexa/Google Assistant will have cloud component to control them (because the smart assistants connect to a cloud end point to do the control). This means you can also use the Alexa/Google Home apps to control them remotely.