One of the ideas of the space station is to prove that man can live in space. So, why aren't they doing this?

as the astronauts/cosmonauts on the international space station have oxygen supplied to them in tanks... growing fruit and vegetables would mean using up some of that oxygen and there would (eventually) not be enough for the astronauts to use themselves for breathing... which would mean that Russia and the USA would have to send more supply capsules more frequently.

Not enough room or the facilities to grow them.

major problems with this.

1. No gravity. Plants would have a very hard time growing at zero gravity. Sprawling may happen.
2. Soil. You would need to keep soil tightly packed so roots could gain nutrients. Containers of some sort might work as long as the plant had room to grow and the soil did not escape.
3. No Sunlight=no PS. Yes, artificial lighting would be needed.
4. Water. I am sure that clean water is at a premium up there.

The best we can hope for, in extraterrestial agriculture, is Mars. With Hydoponic Domes, crops could be grown there easily compared to in orbit around a planet.

Corey M, since when did plants consume Oxygen? Plants consume CO2 and create Oxygen, they are part of our symbiotic relationship. If it could be realistic to grow plants in space, it would solve alot of problems with recycling and waste products.