Microwave ovens might be a bit tricky to adapt a getting the door off could be tricky.
Monitors should be easier, as everything simply unscrews. A couple of safety points though:
1. The capacitors inside TVs and monitors can hold enough charge to give you quite a jolt long after they've been connected to the mains. Handle electronic components carefully ;
2. There's a vacuum inside a cathode ray tube, which means that they implode if broken (with shards of glass flying everywhere). If you need to dispose of a CRT, wrap it in a sack (or similar), stand well back and hit it with a shovel!
Instructions here:
http://www.instructables.com/id/Make-a-Cat-Bed-from-a-Computer-Monitor/
(Click the 'Next' buttons)
Some lovely pics here:
http://www.buzzfeed.com/amandam10/21-really-cool-pet-beds-made-from-old-electronics-1kzg
Chris