I had a hard time finding information about this trail but I decided to check it out. Good call... I was pleasantly surprised by the area's rugged beauty, history, and confusing network of roads and washes. Topo and GPS are highly recommended. Most of the trails run about 1.5 - 2.5.
Dripping Spring is dryfall spring about 6 miles south of the I-10 turnoff (12 miles roundtrip) but with all the various roads, mines, etc I put in close to 25 miles of romp. The area ranges from 1500 feet to 2200 feet and includes a diverse selection of terrain features from craggy ridgelines, buttes and cliffs, rolling hills, slickrock sections and deep, sandy washes. Peaks and spires protrude from the landscape. This region is part of the New Water Mountains (and adjacent to the New Water Wilderness) and is prime desert bighorn sheep habitat. We saw bighorn scat, bones, tracks, and a hoof. Dripping Spring itself is an important lambing area.
We checked out the Gold Nugget Mine, a huge open pit area of sand/gravel/rock (unknown name), the Belle of Arizona Mine, the Apache Chief Mine, and the Poorman Mine. Each of these had its own interesting aspects... for example, the gravel pit area was a good place to do donuts and get some high speed action, while the Apache Chief had a complex network of shafts and corridors, etc. Along the way we passed several old cabins and structures, including a neat old place called the "Apache Chief Bed n' Breakfast" that had some interesting things inside (like a human dummy and lots of trinkets people have left behind) and outside the cabin (like chairs and a fake grave).
The final stretch to Dripping Spring gets 3.0 moderate with some rocky steep sections and an interesting tight "box" stretch of high-walled wash. At Dripping Spring is an old
stone cabin and some Native American pictographs strewn about. The sheer cliffs and general appearance reminded me a lot of the Kofas... which were actually only a dozen miles south. The area surrounding the spring was green.
Overall, it was a peppy trail with plenty of points of interest along the way.
Terrain near the freeway
Recent remains of the Gold Nugget Mine
On the way to Dripping Spring
This is where you drop down and locate the spring to the left
Sorry... no pictures of the spring, rock ruin, and Indian pictographs... you'll have to go there and see it yourself. 
That "Apache Chief Bed and Breakfast"... VERY interesting inside
A section inside the sprawling Apache Chief Mine
Nice landscape... including this spire I call the "Matterhorn"