DEADLIFTS
Nothing else is better for improving back strength and preventing future back injuries than properly performed deadlifts. Go to bodybuilding.com and read some articles/watch some videos about deadlifting and how to do it with proper form. If you have a personal trainer, have them teach you how to do it in person (although I have heard horror stories about some personal trainers not knowing how to do them right, so do your homework first to be safe).
Doing stuff like rows and lat pulldowns is nice, but those things
will not improve your lower back strength like deadlifts will, and it's your lower back (core) strength that will prevent a back injury.
Deadlifts are easily the best because:
1. They force you to use proper lifting form, starting with the legs, and keeping the spine in a safe, neutral position without rounding it out and risking a slipped disc.
2. They use nearly every muscle group in your body, making them one of the most effective strength-building lifts. Want stronger legs? Deadlifts. Want a stronger lower back? Deadlifts. Want a stronger upper back? Deadlifts. Want better grip strength? Deadlifts.
The lower back strength you gain from deadlifts is absolutely unparalleled. Go to any weightlifting or bodybuilding website and you will see that deadlifts are treated with a kind of reverence and appreciation that no other lift enjoys (except maybe squats).
Youtube video for demonstration and explanation of proper form:
http://www.youtube.com/watch?v=cs-wOHN5tdw
Trust me, after a few months of deadlifts you will see exactly why lifters love it. You should only do them once a week, and make sure you increase the intensity of each workout or you won't make progress. Also, it's crucial to eat properly and get enough sleep (your muscles do most of their rebuilding during deep sleep).