Can a gym be built to supply electricity to homes? A moving magnet induces a current in a conductor, then shouldn't we be able to generate electricity through manual labour?
I was thinking about building a gym that used magnets as weights. People would lift the magnets up and down creating a change in flux generating current.
For example; the exercise bikes and the rowing machines would definitely be able to produce a current due to their rotating discs. Also, machines like a squat stand can be turned into a generator because the weight can be turned into a magnet. The key idea is that any machine that can move can turn into a generator to produce electricity for homes.
There should be many gyms spread out along the city like mini power stations. The electricity generated doesn't have to be used straight away but can also be stored in a battery for later use. I am wondering if there will be enough electricity generated to supply homes (if not all homes then a street or two). 
 A: The maximum continuous power that can be generated for an hour by a fairly fit person on an efficient machine like an exercise bike or rowing machine is $\sim 200$ W (olympic-standard track cyclists might manage 400 W).
Let's say that a gym is occupied at any time by 10 people who are doing this kind of intense exercise. Then you might just be producing enough electricity to boil a kettle (kettles are 2-3 kW) and keep the lights on in the gym. Unfortunately there are another 10 people in the showers who have just consumed more electricity than they generated (typical electric shower consumes 8kW, so a 2 minute shower needs 960 kJ = 200W $\times$ 80 minutes).
Does that answer the question?
However, it might be an interesting gimmick to allow people to charge up their phones or other personal devices using the electricity that they personally generate. That would probably be feasible with the right adaptors and transformers.
A: As answered above no not electricity, but usable force has been done.
Treadmills originated as a corn mill powered by prisoners. They would stand on a large cylinder and turn it grinding corn.
A: There is such a project in Paris: the Paris Navigating Gym (link in French). As mentioned in the project, the power of the cyclists is the only one used to move the boat.
Which, in the light of other answers, is hardly possible.
A: Yes, these exist. There's one here in Portland, OR, USA called The Green Microgym. But it doesn't generate much energy. People wildly overestimate how much energy a human can produce.
They claim to "have generated 20% of our own electricity" but it is done by "combining human and solar power". They claim to use "Energy-producing cardio equipment (ellipticals and stationary bikes)". I don't have any numbers for how much of that 20% is human power and how much is solar, but Rob Jeffries already covered what a human is capable of: about 200 W.
If all 150 members exercised a very generous 1 hour a day producing 200 Wh each, and all that energy was turned into electricity with no loses, that's a maximum energy output of 30 kWh. To put that in perspective, a refrigerator uses about 1.5 kWh per day. So 150 people exercising an hour a day at peak capacity with perfect conversion to electricity can power about 20 fridges or about 0.133 fridges per person. That's an ideal scenario.
Most of the gym's efforts go into reducing electricity use and waste rather than generation claiming to have reduced their electricity use by 85% compared to normal gyms (per square foot).

There have been claims of generating electricity using human power before. This is entirely possible, but they generally wildly overstate how much power can be generated.
The most recent I've seen is the claim that "60 Minutes On This Bicycle Can Power Your Home For 24 Hours". This is nonsense. Note the total lack of details about the device in the article or video, they only talk about its potential.
As Rob said, the average person will put out about 200 Wh in 60 minutes. A single LED bulb uses about 10 W or 240 Wh per day.
So, maybe if you live in a shack with one light the claim is true. More realistically, it could be used to charge a phone or laptop or power a radio.
A: There was a BBC program called 'The Human Power Station' that measured this. One hundred cyclists at full pelt just about managed to deliver the power needed for an electric shower... so a gym with a few people gently exercising on treadmills probably won't even keep the gym's lights on let alone export power to any other premises. There's a link here http://www.bbc.co.uk/programmes/b00p8469 but it's not currently available to view... 
A: The Grand Tour just did this. (the guys from old Top Gear) 
They tied all the gym equiment to generators, and probably maxed it out with hired people, and after 8 hours of lots of people working out 
 they charged a GeeWiz electric car to about 30%, so it only went 20 miles.
In conclusion, it's not a lot of energy. It would be enough to charge your phone while you're working out, but you need to invest a lot in the generating equipment which costs a lot more than the normal stuff. So it's not a good investment for a gym.
