+1 for stretching - Great point. Too few people stretch adequately these days.
However I have to disagree a bit with the post dismissing strength training. Strength training in conjunction with stretching is the best bet for injury prevention. Stronger supporting muscles allow for proper form, minimalize our bodies' tendancies to compensate for weak muscle groups. Injuries don't occur solely due to crashes. Overuse and improper form are equally dangerous, and more easily prevented with adequate strength/conditioning.
If you are a dedicated racer, a little extra upper body strenth/size/weight might be detrimental in long climbs, but honestly, IMO, total body fitness far outweighs these concerns for most cyclists. Functional strength has its benefits.
Generally, strength doesn't have to mean bulk. I strength train regularly, and haven't punched over 148-150 lbs at 5'10. You won't get heavier unless you start eating more calories than you burn. You will, however, train your neurons to fire more efficiently, and recruit more contracting muscle fibers. This allows more force to be developed. It's training, not bulking. Don't get scared by claims that lifting weights will make you big and heavy - It's jus not true. 😉
Do lifts that imitate motions on the bike, and activate the same muscle groups. Be sure to strengthen oposing muscle groups such as hams/quads, bi/tri, chest/back to prevent injuries and encourage equal force distribution on your body.
I'd say focus on:
Lunges, IL squats and toe/heel raises for your legs. Try tracing the alphabet with your toes for dexterity and strenthening those muscles that transfer all of your power to the pedals.
Rows, pushups, shoulder presses and curls/overhead extensions for your upper body/arms.
Superman, good-mornings, stiff-legg dead lift for your back.
Leg lifts, 45 side/sides, trunk rotations and plank for your abs/core.
Start slow, and focus on form with each lift. It's not a cardio/calorie burning session, so enjoy really learning the proper movements needed for these lifts. Remember, you are training your muscles' neurons to achieve more efficient motion and strength.
Good luck!