I don't think I've ever built a "completely" new system - every build uses at least a few components from the previous machine. The closest I ever came was my last major upgrade (going from an Athlon Xp 2000 to an Athlon 64 3000 skt 939 system) when I tossed everything but a hard drive, floppy drive (which is now in its 17th year or so), sound card, and DVD drive. Since then, I've had 1 CPU upgrade, 2 video card upgrades, 1 sound card upgrade, 2 HDD upgrades, 2 DVD replacements, and 2 ram upgrades.
I'm coming up on a major upgrade again, as my Athlon X2 4200 is getting long in the tooth, and I've noticed dramatically lower performance in newer game titles. I'll need a new MB and ram to go with a new CPU, and likely a new PSU as well. Assuming the timing works out as I expect it to, the build will coincide with my 18-24 month replacement cycle for graphics cards. I could end up keeping my sounds card and wireless network card, but since both are based on the old PCI bus, I expect I will need to upgrade both of those as well. My RAID 0 array (constructed with 2 1st gen Raptors) is slower than the high performance terabyte HDDs available today, so they will likely be replaced. If I throw a BluRay drive in there, that will replace the DVD burner. Since I won't need a floppy drive to install RAID drivers anymore, the FDD is going to go, leaving me with a case and a pair of storage HDDs (which might only stick around long enough to transfer their data to the new system).
Of course, that's only the plan - reality will likely differ, depending on how much disposable income I have (big factor, seeing as how I am currently unemployed). That would put my system at around 5 years to completely change out all components.