I had my original A1000 sort-of-die on me.. One of the CIA chips went South. But it wasn't fatal, it just made the clock repeat the same 17 seconds over and over like a very short "Groundhog Day" :-) The internal floppy has since died, so it can't boot at the moment.
The power supply in my 2000 failed. But out of my own Amigas, that's about it. Since I worked in an Amiga service shop for a while, I saw a lot more failures there...