Contrary to many others, while I enjoy cycling (100+ miles/week, 3 or 4 centuries / year), it is only part of my overall fitness plan and goals, which includes upper body strength, core strength, leg strength, low body fat, and endurance and cardiovascular capability.
I chuckle when I read of those who propose minimal to no weight training and even less upper body training. Some would have you believe that the only way to fitness is through cycling and cardiovascular machines. My brother, alas, is in that group.
Of all the pro athletes' physiques, the one that impresses me the least is the pro cyclist with his non-existent upper body, minimal biceps and triceps and 160# weight. Yes, they have great legs and are lean. But, what do they look like with their shirts off?
My training revolves around achieving the body style that I find most desireable, the middle-weight boxer. Toward that end, I taylor my gym time to include free weights and machines and it has paid off toward this end (15" biceps, 48" chest, 10 pullups, and 225# (with 5 reps) bench press).
Unless you are a pro cyclist, I think most fitness afficionados, including cyclists, would be well advised to pursue full body workouts.