Colorado is almost certainly the least wild of the western states, but luckily there are some fairly remote areas left.
The core of the Weminuche is the most remote and wild area in Colorado if the criteria of the maximum straight-line distance from the roads is used.
Even so, in some ways some of the parts of Dinosaur National Monument feel more remote to me even though they aren't quite as far from any roads. The terrain there is very rugged, so there is no such thing as a straight-line distances and the amount of time it takes to get into some areas is staggering.
For example, it took me
three years to find a viable route up to the valleys, canyons, flats and crags around Outlaw Peak. The area is remote enough that while we were exploring the canyon after climbing the peak, we discovered what turned out to be one of the world's largest arches in a place that likely hadn't ever been visited by anyone before 2006. You can read something about it below:
http://www.summitpost.org/article/272889/the-discovery-of-outlaw-arch.html
As remote as it is however, the canyon systems just east of there may be more remote. I spent several trips over a period of six years to find a viable route in. I was unsuccessful and put the project on the backburner, but maybe some day......
Anyway, I've been exploring the area for well over two decades now. I've run ito people on the pretty well know hikes of Harpers Corner and Jones Hole. Outside those areas in the other 25 years or so, not only have I never ran into another person, but I've only found one cairn in the entire region and have never found even one footprint.
Outside CO though, I've been into many more remote areas than this so they do exist if you look for them.