I covered my thermostat with a box picture frame given to us as a Wedding gift. I used a simple 3-screw, swinging brass bracket to secure it to wall. Much cuter! PS It doesn't mess with the internal temp readings of our home, but I would be careful with this. A thermostat that produces some heat should probably not be covered.
Cover up an ugly alarm control panel. I did this with a cheap piece of art from TJ Maxx that fits, some hinges, and a magnetic catch so it stays closed. * I originally planned on painting it with chalkboard paint so I can write reminder notes. That may still happen when I get tired of it. Or paint it the color of the wall so it disappears.