As Road Raven said, warming up and cooling down are very important. I find that it takes me about 9 miles to warm up, which seemed high until I read RR's age/minute correlation (I'm 38). I'm bad about cooling down on weekday training rides, mostly because the light is often failing and it's time to pack in it. I try, however, when possible to ride to weekend rides so that I have a built in cool down.

Having run for the first time this past Sunday in 13 years, I cannot imagine using running as a way to avoid muscle strain or pulls. I can barely walk right now. I did, however, go to yoga last night as per usual. That's my official cross-training. Granted, not all yoga classes or teachers are created equally. You can easily overdo it if you don't know what you're doing and/or when to back off from a pose. That said, it's an excellent way to work on flexibility, balance, and strength. Thanks to the regular hamstring, calf and hip flexor stretches that I do, I largely avoided some of the lower back pain that plagued me when I first started riding.