My wife hates when I leave the remains of guitar strings laying around the house. She especially hates it when they are embedded in the carpet waiting to puncture a bare foot. I personally loosen, then cut them near the end where they are all bent from the post. I throw out the "ends", and then coil the rest of the string tightly so they don't come unwound in the trash can and stick through the side of the bag. It's a skill only a guitar player could appreciate.
Also, I change one string at a time, with the guitar still tuned. I feel this keeps the tuning, intonation, relief, etc relatively unaffected.