Many early computers use ones' complement to represent some kind of signed integer. Examples include the PDP-1, the CDC-6600, and many other popular computers.
The C standard is obviously written with ones' complement machine in mind; for example, it specifies that a signed integer may hold values -32767 to +32767.
But I find that modern day examples of computers that use ones' complement rather hard to come across. I think it's safe to assume that anything you've got that runs a computer program and has signed integers of some kind uses two's complement. So what is the reason for the decline in popularity for ones complement architectures?