Best solution for compact wiring on stripboard

Wiring by Markus Gritsch

Fine (34 AWG) solderable enamel wire (aka solderable magnet wire), isn't enamelled but is coated with polyurethane, etc. No stripping required, soldering turns the polyurethane into a flux and exposes the copper.

Wire wrapping with a proper tool is actually a great technique for building one-off circuits with lots of DIL ICs on. It's easier if you use sockets: http://www.jameco.com/1/3/dip-wire-wrap-ic-sockets although it adds to the cost. It can be less time-consuming than soldering thousands of joints by hand, too.

http://makezine.com/2009/07/27/lost-knowledge-wire-wrapping/

Back in the day people used some sort of 30awg wire for this job. But instead of a proper insulation they had something like a thin layer of colour. The problem was that after some time using the pcb this insulation would break and you end up with errors again. This is maybe why no one uses it these days.

The closest you can get might be transformer or coil wiring. https://en.wikipedia.org/wiki/Magnet_wire

Or you try something like this http://www.adafruit.com/product/1446 They even speak about the old day methods there.

Or you wait until the next 5 people suggest to make a pcb. ;)