4 Wheelin'
Old Dale Road
A word to the wise: Old Dale is an asshole. My friend was really angry with me for making him take his stock Jeep Cherokee on this road.
Before I say anything about how fun this experience is, you'll need a high-clearance vehicle with 4 wheel-drive to even attempt it. Anything less, and you might as well kiss your car goodbye.
I'd also HIGHLY recommend a set of tires that are designed for off-road conditions. This is a challenging trail with a lot of sharp rocks that seemed more than capable of puncturing a standard tire (which we had). Even with a 4-wheel drive Jeep Grand Cherokee, we were nervous that we had bitten off more than we could chew with this road.
Even more importantly, this trail has zero cell phone reception, with no feasible way for a tow truck to navigate the terrain itself, let alone haul you off if something goes wrong. Proceed at your own risk, and have a backup plan in case you encounter any car trouble.
Directions - For those of you with off-roading wagons, Old Dale Road is a great place to test them out. Take Pinto Basin Rd. past White Tank Campground, and follow it down into the Colorado Desert section of the park toward Cottonwood. When you see the turnoff for Old Dale Rd., make sure you hang to the left at the fork to avoid ending up on Black Eagle Mine Rd.
Resources
NPS.gov - Joshua Tree Backcountry Roads