Wakeful uses the Android WakeLock api to prevent your phone from sleeping as long as it is activated. There is a persistent notification while it is activated so you don't forget it is on, and it automatically deactivates itself if you manually turn off the screen.
Wakeful is deliberately simple and does nothing other than stated. There is no analytics, no tracking, no weird permissions, just a little icon that keeps your screen on until you turn it off.
This app is open source, check it out on github (the link is listed as the website in the contact details).