You weight lifters are crazy! I can barely bench press my weight, can't handle more than fifteen pound dumbbells (last time I tried) and would not even think about doing pull ups with weights.
For chest I do wide push ups, triangle push ups, dips, wide grip pull ups or resistance bands. For shoulders I do diamond push ups, close grip pull ups and military press push ups ('Chinese' push ups). For core I do leg lefts and butterfly/flutter kicks (on the ground) and knee raises (from the bar). Of course, I don't concentrate on a muscle groups that often (hardly ever) but do circuit training, super sets, etc, and work my whole body every routine. I will place emphasis between strong man strength, endurance strength and explosive strength though, because all three are necessary for functionality, at least in experience and opinion.
Plus, calisthenics keeps me lighter on my feet, more flexible and away from injuries (I've injured myself twice from improper lifting and never from calisthenics... I guess it's different for everybody).