I've had a few computers of my own break after a few years of use, and I've seen computers owned by friends and family do the same thing. They either slow down (even running the original software they shipped with) or crash more often (kernel panic/BSOD, freezing, etc). All computers eventually fail, and not always in easily explainable ways.
For example, my first computer was a MacBook Pro. After about 3 and a half years of use, it started to freeze a few times a week, then reliably every day. OS X would stop responding; my mouse moved, but absolutely nothing responded. It ended up lasting more than four years, but I was in the habit of saving my work every time I paused in typing, and kept rigorous backups.
I've also seen old family computers running early versions of Windows completely freeze (no mouse movement) just after completing startup. And I've seen a 4 year old 12" PowerBook G4 run like molasses even after having been wiped and reset to factory settings and OS.
What causes this? Do the electronic components break down over time?