Is it ever appropriate?
It is used in agricultural fencing (see Wikipedia:Barbed wire #Agricultural fencing) agriculture. What alternative methods or technologies can be used to avoid needing to use this?
It is sometimes used in fencing in urban environments, to prevent trespassing, especially where there are no building and safety standards to prohibit this, and where crime rates are perceived to be high. "Soft technologies" can reduce the need for this, e.g. mixed use development and design of pathways and entrances so they are always visible from the windows of residences and from areas of high foot traffic.