Who makes budget speaker cables which are truly “good” or “exceptional” in quality?

Agreed that many “budget” cables can make this list...and that’s the fun of discovery. My fast vote for Budget is Signal Cable. Silver Resolution Speaker Cable. 

(Higher vote for the AC Silver Resolution Power Cord.) Might add that the other matching Silver Resolution Cables are Fabulous. 

Price and Performance are Excellent. ...will they compete with “ultra” Cardas, Straight Wire, Kimber, Nordost, Transparent, NBS, Acoustic Zen...the Answer is no. 

But Count me in on Signal Cable Silver Resolution Products. “Bravo!”

With a little DIY-efford you can make the second best cable I have ever known/auditioned (the best was a solid silver wire by the Swiss company Audio Consulting, very pricey..., thread in a cotton hose).
It consists of 6 solid cores of bell wire in a PVC coat. So twist 3  opposed leads each and crimp with a cable lug/cable shoe, cable termination or whatever you need. You will get a cable that will outperform nearly every cable of the big names! Build with confidence- this cable won't disappoint you!

I have used many different cables from many companies. After over 55 years of audiophile fun and games I now use AWG10/type3-k tinned marine mains wire. Type 3 has greater strand count and k is for awg30 individual strand size. It can be had at reasonable per foot cost (under .50) and has superb audio characteristics. All interconnects and speaker wiring has only one goal, to transmit the signal with no alteration. If a connect is adding some "voice" to the sound then for me it is unacceptable.

You all have been brainwashed, imho

That's humble alright (third meaning).