Did you know that 60% of most animals and plants is water? More than 70% of the Earth's surface is covered with either water or ice (another form of water). Despite the way freezing works for most substances, water actually expands when frozen beyond 4°C, thus allowing ice to float over the surface of water and enabling subsea life, by providing insulation against cold temperature for everything underneath.
Due to nature of questions I’ve received, let me try to cover this topic under a number of questions, instead of doing it the usual way. Also, please note that naturally, water contains minerals, dissolved gasses, etc. Some of the discussions and all of the values presented below are about fresh water, as for example by addition of salt water density is increased and behaves totally differently.
Density of water at room temperature  (roughly 20°C) is equal to 0.9982071 kilograms per litre, but it varies with temperature. To get an overall idea about the variation of mass density of water with temperature see the graph below. For the density of water at different temperatures, look a little bit lower into the article, for the table.
As also can be seen on the “Water density graph” below, liquid water reaches its maximum density at 4°C, where water density is roughly equal to 0.999975 kilograms per litre. As temperature moves away from that point, water gets less dense.
Although water ice (hexagonal ice) is less dense than liquid under atmospheric pressure, under influence of increasing pressure, ice transitions to other allotropic forms (ice II, ice III, high-density amorphous ice (HDA) and very-high-density amorphous ice (VHDA)) with higher density than liquid water. For example, Ice XII is 1.3 times more dense than water. Additionally, an isotope of hydrogen (deuterium) can bond with oxygen to form heavy water (D2O), which is denser than pure water.
What is the specific gravity of water?
Although the definition is broad, generally the term is used specifically to reference ratio of density/mass to that of water, in the case of liquids and air in the case of gases. The broader term is known as relative density. Specific gravity becomes important for any substance when you are to understand whether it will sink (specific gravity lower than 1) or float in/over water (specific gravity bigger than or equal to 1). As the reference fluid is water itself, the specific gravity of liquid water is 1 at all times.
What is the specific weight of water?
Specific weight of water (aka unit weight of water) is defined as weight per unit volume of water. Basically, to calculate specific weight water density at specific temperature is to be multiplied with acceleration due to gravity. As the formula includes the acceleration term, specific weight (just like the weight itself) is dependent on the gravitational force and consequently varies from one planet to another. Specific weight of water on Earth at 5°C is 9.807 kN/m3 (62.43 lbf/ft3).
There are a number of ways to find density of water, including industrial densometers that will employ different methods (nuclear, coriolis, ultrasound, microwave, and gravitic) to give out the density of the liquid. The simplest tool that can be used for this purpose is called hydrometer. It consists of a cylindrical stem and a weighted bulb that floats inside the liquid. For more dense fluids, bulb goes up, while for less dense ones, it goes lower into the fluid. That way it is easy to read the density of the fluid using the scale on it. Although hydrometer might sound to be a very simplistic instrument, it is widely used to measure amount of fat in the milk.
Density of liquid water is largely dependent on temperature. As such, it is impossible to define a single value for the density of water. In engineering, density of water is generally calculated using specific volume of water. For the range of density values, please refer to the water density table below:
When water melts, dependency of its density on temperature sharply reduces (almost 1:5) and becomes roughly linear. Ice density hits 0.9162 kg/l and changes only to 0.9257 kg/l until -100 °C.
First of all, please note that density is equal to mass (doesn't change) divided by volume (changes with temperature). Generally, when the temperature of the substance goes up, the vibration and relative motion of molecules increase and volume changes. That's why as a substance melts its density drops (molecules have more freedom), when it freezes its density increases (molecules are packed closer together and can't move much).
In the case of water, hydrogen and oxygen atoms are bonded with a covalent bond, while molecules are bonded with a hydrogen bond (which is considerably weaker). When water freezes, it crystallizes into a rigid lattice, effect of hydrogen bonds increase and for each molecule the number of bonded molecules goes slightly up, creating gaps in between. That's why upon freezing water actually expands by (roughly) 9%, consequently reducing density.
 STP (Standard Temperature and Pressure - 0 °C, 1 bar) and SATP (Standard Ambient Temperature and Pressure - 25 °C, 1 atm) are different from room conditions. As liquids are incompressible, pressure variation does not have any considerable effect and temperature should be considered only. Density of water at 25 °C is equal to 0.9970479 g/cm3, while it's equal to 0.9998425 g/cm3 at 0 °C.