I had a big discussion on this in the cyclingplus forums. Basically it sounds like strength has little effect on cycling. It is a weight supported exercise, and those who weight lift during the winter find that they lose most of their muscle in the cycling season. It is primarily aerobic strength that is needed.

While I believe this is all very true, I weightlift, mostly because I have a gym membership that I like to take advantage of. I work on my upper body, and hamstrings. I haven't seen any visible effect on my cycling from this, and if you're a spinner I think you'd see even less benefit.