I know that feeling, I would describe it as "robust". A chunky, solid feeling. But I would classify DVI and VGA the same, along with parallel ports, DIN (but not mini-DIN), and basically all mains power connectors.
At the opposite end are USB (especially micro), HDMI, 1394 and other dainty connectors that feel like they would break (and they do) if you don't take utmost care in mating them.
That being said, I don't think it's a feeling unique to "old" connectors; besides the mains plugs mentioned above, modern industrial, military, and avionics equipment connectors remain equally satisfying to mate. It's just that most consumer equipment has sacrificed robustness for compactness and cost.