Lifting weights properly is safe. Period.
I get more than a little irritated when people complain about lifting weights because "it is not safe." The reality of life is risky. Driving a car is not void of serious risk, flying in an airplane is risky even playing soccer or peewee football is surely risky behavior. There is risk in everything we do and that is just part of life. The activities I listed all risk of some sort of accident and when that accident occurs it is going to much more catastrophic than something that might happen in the weight room. The weight room offers so much more control than the open road or the playing field. Spotters are available, safety stop bars are on all racks, and properly taught exercises are simply weighted versions of normal human movement. If a squat were unsafe we would all be in danger of getting off the toilet everyday unless we had a cane, a deep squat for a lot of people is nearly the same thing as sitting down and getting back up off the toilet.
Lets review some actual research. In the book Starting Strength a table is contained in the back that shows injury rates from many different sports. This data comes from the Journal of Strength and Conditioning Research published in 1994 in the 8th volume and 1st issue, pages 53-57. I got a copy of this article from the University of Iowa library's article delivery service and read it for myself. In this study surveys were taken from secondary school instructors/coaches who were asked to report the number injuries sustained while participating in a given sport and the number of hours of participation. The results were astounding to say the least I'll list a few of them, reported as injury rates (injuries/100 participation hours). To clarify weight training means using resistance as an exercise method, powerlifting is a sport in which the Squat, Bench Press and Deadlift are contested, and weightlifting is a sport in which the Snatch and Clean and Jerk are contested.
Soccer = 6.3
Basketball = 1.03
U.S. Track and Field = 0.26
Football = 0.1
Tennis = 0.07
Gymnastics = 0.044
Weight Training = 0.0012
Powerlifting = 0.0008
Weightlifting = 0.0006
Isn't it shocking that Soccer, the most popular sport for kids, is the most likely to cause injury? I thought so, until I really thought about it. In soccer, I am talking about youth leagues here, a group players are cleated on some sort of turf and told to run full speed after one single ball. The coaches and parents are at the sidelines where they shout at the kids trying to tell them what to do next. This is a recipe for disaster. Inevitably kids are going to collide, uncontrollably, cleats will get stuck in the turf and kids will fall all over each other. Sprains, cuts, bruises, and broken bones are all invited to the party. Remember this is probably the most popular sport for kids to play.
Lets contrast this with lifting weights. In the weight room a kid is lifting weights and inches away is a trained spotter, either the coach, a parent or another trainee who has been trained to help lift the weight when the lifter can't do it alone. The lifts are watched by the coaches and cues are shouted out to remind the kids to keep their back in straight or their knees out or whatever the need to do to maintain proper and safe lifting form. The weight on the bar is known, it is planned out ahead of time how much weight is on the bar and everyone who can do simple arithmetic can see if the bar is loaded properly. Weight training is often regarded as unsafe. In light of actual data and thought this assessment is ridiculous.
I think part of the fear is that it is hard. This is really dumb because on that basis "advanced" math like calculus and partial differential equations should be unsafe for the brain. I have taken high-ish level math courses and they are hard but my brain adapted and now those principles and homework problems are not so hard. I remember my first squat and bench press with 185 lbs. It was hard and felt really heavy. Now that I have progressed past that weight I am stronger and it is easy to lift. That is the point of heavy weights, to make you strong. You don't get strong, mentally or physically, without challenging yourself with hard things.
Perhaps another reason lifting weights is considered dangerous is all the blockheads in your local 24hr fitness or Golds Gym, and university and high school weight rooms. We have all seen the sleeveless guys lifting too much weight with terrible form all the while grunting for everyone to hear. This same guy can't look over his shoulder because he hasn't lifted with full range of motion exercises, and certainly has not thought about mobility in general. These guys are the meatheads. They are self taught lifters using bodybuilding magazines as textbooks. You wouldn't trust your car to self taught mechanics, or your body to a self taught doctor. So don't asses the relative safety of lifting weights by theses guys and certainly don't get trained by them.
Lifting is safe if you do it right. You are responsible to do it right. Learn how from a good coach. If a "coach" tells you to do half squats instead of full depth squats they are probably not a good coach. Limiting knee flexion by half squatting has no basis, but that is a whole post in itself. Anyway if you want a good coach I suggest using the starting strength certified ones. You can find one nearest to you here. If you are confident in learning by yourself or with a friend use the Starting Strength book and DVD, take videos of yourself, and get the form down.