Yes it's possible.
An obvious example would be a Remote Access Trojan (RAT). Once your computer is infected they can do essentially whatever they're set up to do. This includes monitoring your screen, logging keystrokes, and accessing webcams.
My personal experience with this was being infected with the Blackshades RAT a few years ago. I was monitored for about two days and on the final day the kid on the other end clearly got impatient with me and demanded to know multiple credentials via a chatbox he put in the middle of my screen.
My solution at the time was to remove my usb wireless card to prevent him from sending any further commands, format the computer, and reinstall from scratch.