I don't think it is necessary to spend a lot on hookup wire, but it is worthwhile to use something of high quality. Of course, if the wires are short the problems are minimized.
Sometimes it isn't the wire itself so much as the insulation that makes the audible difference. PVC, for example, has much higher dielectric absorption than teflon. The insulation stores a slight charge from the audio signal and releases it back into the wire as the signal voltage drops. It is good to minimize this.
In some circuit locations, different wire can make a significant difference. One place that comes to mind is the connection from the input pot's wiper to the first grid pin (or input pin if it's one of those eight-legged critters). If you minimize this distance, which you should do anyway, this will of course become less critical.
One of my favorite types of hookup wire comes from disassembling Belden 1585A CAT-5 cable. Removing the jacket reveals four twisted pairs of 24-gauge teflon-insulated solid-core copper wire. I untwist the pairs and straighten what's left of the twist kinks. Not expensive at all.
I also use Vampire continuous-cast copper 21-gauge solid-core copper from
http://www.percyaudio.com. This stuff is coated with clear polyethylene, sort of like magnet wire. I slip teflon tubing over it if high voltages are involved. It costs maybe $6 per fifty feet, if I remember right, and is excellent quality.
For all-out projects like my Aurora amps (can be seen at
http://www.aloha-audio.com/triode1.html), I used teflon-coated pure silver wire from
http://www.silveraudio.com. But even that stuff doesn't cost all of $5 per foot.
Honestly, I don't mind spending a few dollars per foot for good hookup wire. I value my time enough that I don't want to waste it on junk. But good hookup wire doesn't have to be all that expensive.