What program are people using these days for 3D stuff?
What program are people using for 3D artwork? That's a pretty open-ended question. Try Google for "3D drawing programs."
You'll find plenty of alternatives, including freeware like Google SketchUp and open source like Blender, flash-centric vector renderers like Swift 3D, CAD programs, and conventional-wisdom 3D artwork modelers / renderers, some with 2D vector rendering add-ons like Cararra. The vast majority provide try-before-you-buy demos. (And all of them are being used by people.) Try some and choose your poison.
There really is no mainstream program that does what Dimensions did. There are some that render to 2D vector artwork, but all that I've seen do so by resorting to drawing facets of a surface, not by generating blends inside clipping paths as Dimensions did. And that may be fine, if all you want is the final render as-is. But it's less versatile for post-editing.