Regarding plain old water tiles, the ones that have no resources on them - their yield is poor, and there is no way to improve their yield besides building a Lighthouse for food and the Colossus for gold. Those tiles should generally be lowest on your list of priorities to work.
It isn't like Civ3, where all coast tiles produced two food by default, and then, besides the Harbor to increase food output by 1 for all water tiles (like Civ5's Lighthouse), there was also the Commercial Dock to increase gold output by 1 for all water tiles, and the Offshore Platform to increase production output by 1 for all water tiles. Civ5 has no equivalent of the latter two buildings, so generally coastal cities are not as effective in Civ5 as they were in Civ3.
The change is that in Civ5 there are buildings (Harbor and Seaport) that increase the output of water tiles with resources, but not bare water tiles. So water resources are a lot more important now. Generally coastal cities should only be built if there are several resources in the water, as others have mentioned.
to every water tile. Harbour doesn't give gold, but it does increase your overall gold output in the city by 15% with no maintenance, which is cool. Harbour and Seaport still grant more hammers and gold to resources. Overall, 1 tile islands become much more viable.
