It is possible that many years from now we could be treating sea water to use as a drinking water supply. This might happen if climate change continues. Lets hope we fix the climate change problem before this!
So desalination as Jake said, is actually already used in parts of the world. The big issue with using sea water for drinking water is that the energy required for desalinization is higher than cleaning fresh water. I found an article that suggested switching the US from fresh water to desalinized water would increased energy consumption by 10% for the US as a whole. Considering that most countries are not using renewable energy sources 100% of the time, desalinization would increase fossil fuel emissions and make the problem worse. For countries like Singapore, Saudi Arabia and regions in the US, access to fresh water is an issue, but the focus should be on reducing the environmental impact of the desalinization and only using it when the alternatives are not available.