Well..Hmm...Let's start here:
The Principle of Specificity, as defined by the American College of Sports Medicine, states, "Sports training must be relevant and appropriate to the particular sport an individual is training for in order to produce a training effect. For an athlete to become better in a specific sport or a specific skill, the athlete must perform that sport or skill."
However, most cyclists are time crunched (Myself included, you may think "Chad you are around cycling all the time!" Well I am// but if I'm commentating for 6 hours and transferring to another stage or race and doing this the entire summer, cycling takes a back seat many times). The best way to stay FIT is well..to run/jog/walk if your time on the bike is severely limited.
If you are a avid cyclist and are wondering if running helps: It does and doesn't. First of all running fitness and cycling fitness are different animals. If you are looking to be just FIT...then you can acknowledge the fact that running helps you stay fit. (I usually drop 5-7 lbs when I pick up running for 2 months)
Research indicates the running requires a greater oxygen uptake so in essence you may be a bit more "Fit" as a runner than a cyclist. The translation however, is a bit more complex. Yes, I believe you can translate some of the fitness over to cycling but to become a better cyclist, you have to be "sport specific". For example, doing hill repeats on the run won't necessarily make you a better climber on the bike. You have to get out and CLIMB on the bike. Recruit the muscles needed to get your arse up that climb. Same with sprinting, pack riding etc. NOTHING can replicate that except...well..cycling.