Hi - I've ridden it on a loaded tour, in late July 2005. I would recommend it, it is beautiful.
The west side ascends up a green forested valley, then ascends above tree-line into high alpine meadows. The last several miles are fairly difficult, mostly because of the altitude, there is nothing terribly steep - I think it's all 6-8% grade at the steepest. The descent down the East side was fast, smooth and open. The road has some narrow sections on the West side maybe 15 miles out of Aspen. Don't ride it on the July 4th holiday weekend, because there will be too much traffic, and if you can do it on a week day that would probably be better, but I would ride it again, it's not too dangerous.
The weather in July is excellent, cool mornings and warm sunny days -- but there are often afternoon thunderstorms on the high passes. It would be good to be at the top of Independence Pass by noon or 1pm to avoid thunderstorms. Thunderstorms usually start around 1-3pm and can last a few hours, then they go away. Although short, they can be severe, with lightning, hail, rain and strong wind.