Wire-wrap is still a useful technique for some situations. I use it mostly for low-frequency test jigs, test adapters, etc. - situations where I need something right now, and once it works, it will get heavy use, so it must be reliable. At the moment I have a situation where there are no PCBs, just a bunch of connectors fastened to thin steel plate.
Connectors with wrire-wrap terminations can be expensive, or simply unavailable. In the case of D-subminiature connectors, I get parts with the straight PCB pin termination, then wrap to the (round) pins and solder. The soldering needs a deft touch, otherwise the kynar insulation can peel back from the heat. You get the hang of it with practice. As noted by another poster, the wrap gives strain relief.
A few times I have run out of links for 0.1 inch headers on evaluation boards, so I wrapped the (square) header posts instead. Worked fine.