Our expert says:
Yes, absolutely, though it depends on what your goal is from strength training. If you just want to develop a base level of strength, then body weight is more than enough. If you want more, and wish to improve performance, or power, then you probably need other weights.
As for the back, it's not too much of a risk doing a push-up, unless you really have a weak core and arch your back excessively. But it's not a major risk. Other exercise, certainly, like situps and if you did a bench press, then you have to be careful. Technique is obviously important, both for preventing injury and getting the right result from the drill.
I think if you are serious about strengthening up and building muscle, however, you might wish to get some kind of additional equipment, only because you are quite limited doing only body weight training. If your goal is simply strength, then pushups, situps, tricep dips, squats, lunges, calf raises, and some pull-ups provide a pretty good overall workout.
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