What’s the maximum weight capacity on standard weightlifting equipment (bench, squat machine, deadlift cage)?
There’s not really one standard. Every manufacturer has their own approach and they want theirs to be different than everyone else’s. Machine capacity will be different than free weights. I don’t lift particularly heavy weights but a Hammer Strength chest press machine can probably hold about four large plates on each side, so maybe 360 pounds. A barbell may be able to hold more. This machines uses free-weight weights. Machines with their own plate stack usually have lower capacities.
The closest you’ll get to a standard is with olympic style barbells. Even then, the style of plate will determine the maximum capacity. That said, I have seen as many as 8 45 lb plates per side (~765 lbs) at the gym, but if you use 100 lbs plates, as they do in most power lifting competitions, you could easily squeeze over 1000 lbs on one.
For other equipment, it entirely depends on the design of the manufacturer. For instance, I think most leg press machines will cap out around 1000-1200 lbs, but I’ve also used ones that have a higher capcity up into the range of around 2000 lbs. And, as CookingWithGas points out, those with their own stacks built in will likely have a lower capacity, generally only a couple hundred pounds.