The first disadvantage of having no gravity is the bones and muscles of any life would become nearly useless. As you can see with astronauts coming back from missions in space they are weak and need therapy to gain back their muscle strength and bone density, they are also more likely to get diseases like osteoporosis. Another disadvantage is the lack of control over objects. For example, with astronauts in space they must use caution eating certain foods that could cause a catastrophic failure to their ship if something as simple as a crumb gets in the wrong place resulting in the possible death or even destruction of the ship. The possibility of losing control over something even larger due to lack of gravity could be even more catastrophic. The best advantage in my opinion though is the capability to move, hold and throw heavy objects with ease when necessary. There are many cases on earth that if we could move larger and heavier objects without the use of heavy machinery it could help so many different things happening around the world. It could even reduce the use and production of energy because there would be so much less need for us to use heavy duty machinery. Another advantage would be the pure fun of it. Being able to basically fly, jump really high, the possibilities of having fun in zero gravity are nearly endless. I probably would not want to travel in space though. I think the possibility of danger is too much of a risk and I think I would get bored fairly fast starring into the vast emptiness of space even if we were able to visit many other planets.
