Is wire wrapping still used nowadays?

Occasionally, in some R&D lab, maybe, if they really need a one-off prototype and someone knows how to wire-wrap and has the tool and wire, and reliability isn't important. Otherwise making multi-layer PCB has just gotten too cheap and easy for everyone. Of course, multi-layer boards are much harder to fix than a rat's nest of thin wires, but with modern EDA software, are far more likely to be correct in the first place.

In some parts of the world where financial limitations and difficulty of access to markets force people to make do with whatever they have, it's no surprise to find old techniques in use. But google turned up no concrete anecdotes like that for WW. (Maybe I didn't spend enough time googling.)

More likely, WW is to be found in use by hobbyists with an itch to go retro, for example http://hackaday.com/2012/07/10/16-bit-hcmos-computer-is-a-wire-wrapping-wonderland/ where one commenter states "It’s rather zen, and an enjoyable way to burn a day – like knitting, basically."

Wire wrap isn't used much today for a few reasons, but perhaps the most important is density. It's not possible to pack wire wrap connections much closer than the classic 0.1 inch spacing, which means you can't have as many connections on an IC or board of a given size. Applications which demand high reliability usually demand small size as well, so multilayer (often far more than 8 layers) printed wiring boards are ubiquitous.

Another consideration is the amount of skilled labor needed. A surface mount printed circuit can be assembled almost entirely by machine, while even the most automated wire wrap systems still need manual intervention. Once the printed circuit assembly line is up and running, the defects are minimal and can be monitored statistically. It's much harder to ensure quality with an army of humans holding wire wrap guns.

There is one place where wire wrap, or at least the wire used for it, hasn't died: white wire (a.k.a. green wire) fixes. The first iteration of a board often has a few design defects which get fixed in the first copies of the board by cutting incorrect traces and making a correct connection by soldering down pieces of wire wrap wire.

I frequently use wire wrap techniques to make quick connections between eval boards and similar pre-pcb prototype setups. Most .100" headers/connectors (and even with care the 2mm variety) will take a single layer of wrapping just fine. It's cleaner and no more time consuming than soldering, and doesn't leave any residue behind when removed. Sometimes one end of the wire will end up soldered into a via or directly to an SMT pin, but the other may end up wrapped onto an available header pin.

Frankly I suspect this is why the tools and wire are still fairly widely available, even though long-pin wire wrap sockets and headers seem to be scarce.