Previously I've taken the same case, and upgraded the parts I wanted to change out... so at first all I changed was the RAM, then I changed the CPU, then I changed the GPU 2 times, then the motherboard died and I had to go build a new one so I kept the GPU, PSU and Case and bought a new motherboard CPU and RAM and hard drives...I guess i've had the same DVD drives/burners since 2004 but after I install the OS I barely use the drive anymore.
There is no 'average' here or any common ground... it could be "everything but the case" or it could be "just one part".
I usually keep my mouse, keyboard, and monitor. However, on occasion, I'll keep my case, power supply, and/or hard drive.
The past number of systems I've built for myself, I've sold my old computer off to my parents, so there really isn't much I can keep.
I think my next system I build in probably 5 years or so, I might keep my power supply and case along with mouse, keyboard, monitor. Hard to say though. 5 years is a long time. I think my system will hold up nicely for that long or longer.
Don't lie to someone who trusts you. Don't trust someone who lies to you.