The hydrogen bond between water molecules is the reason behind two of water's unique properties: cohesion and adhesion.
Cohesion refers to the fact that water sticks to itself very easily. Adhesion means that water also sticks very well to other things, that is why it spreads out in a thin film on certain surfaces, like glass. When water comes into contact with these surfaces, the adhesive forces are stronger than the cohesive forces. Instead of sticking together in a ball, it spreads out.
Water also has a high level of surface tension. This means that the molecules on the surface of the water are not surrounded by similar molecules on all sides, so they're being pulled only by cohesion from other molecules deep inside. These molecules cohere to each other strongly but adhere to the other medium weakly. One example of this is the way that water beads up on waxy surfaces, such as leaves or waxed cars. Surface tension makes these water drops round so they cover the smallest possible surface area.
Water's hydrogen bonds are also why its solid form, ice, can float on its liquid form. Ice is less dense than water because water molecules form crystalline structures at freezing (32 degrees Fahrenheit or 0 degrees Celsius) temperatures. The thermal properties of water are also linked to its hydrogen bonds. Water has a very high specific heat capacity, which is the amount of heat per unit mass required to raise its temperature by one degree Celsius. The energy required to raise the temperature of water by one degree Celsius is 4.2 joules per gram. Water also has a high heat of vaporization, which means that it can take a lot of heat without its temperature rising much. This plays a huge part in the climate, because it means that oceans take a long time to warm up.
Water is often known as the universal solvent, which means that many substances dissolve in it. Substances that dissolve in water are hydrophilic. This means that they are as strong or stronger than water's cohesive forces. Salt and sugar are both polar, like water, so they dissolve very well in it. Substances that do not dissolve in water are hydrophobic. This is the source of the saying “oil and water don't mix”. Water's solvency is why the water that we use is rarely pure; it usually has several minerals dissolved in it.