A few follow up questions:
1. If I were to go to a 27" monitor at a higher resolution, I would only need a single dual-link-capable DVI cable, right?
The physical size of the monitor has nothing to do with it, it's all about resolution. Higher than 1920x1200, dual-link DVI required.
2. And if I were a really bad glutton, I could still run two 27" monitors at high resolution off of one graphic card (requiring a total of two dual link-capable cables), right?
Not quite sure what you're asking, but a single card with 2 single-link DVI connections can handle two monitors, each running at up to 1920x1200. 2 dual-link DVI connections can run two monitors with higher resolutions.
3. I just need to check to be sure my two-plus-year-old GeForce 8600 (I think, but I'm at work now) card is capable of Dual Link DVI (and not merely "Dual DVI"), correct?
I don't think my card is capable of this because it's on that cusp-of-age and it only has one DVI port; the other is VGA.
I think you're 8600 will be a dual-link DVI. I think my 7800GTX was the last generation of single-links.
Intel i7 4790k @ stock, Asus Z97-PRO(Wi-Fi ac), 2x8GB Crucial DDR3 1600MHz, EVGA GTX 760
Samsung 950 Pro 512GB + 2TB Western Digital Black
Dell 2408WFP and Dell 2407WFP-HC for dual-24" goodness
Windows 10 64-bit