High heeled shoes are one of the most popular types of shoe, and are worn the world over. They also have the added benefit of making you look taller, which can be advantageous for shorter people. There are several problems with high heels though, which is the reason that more women don't wear them regularly.
The biggest problem with high heeled shoes is that they are often hard to walk in, even with practice. They tend to focus the entire weight of the body onto the heels which makes balancing a lot more difficult. This also puts more of a strain on the legs and ankles and can result in aching muscles and sprains. Not to mention that they often become painful after a few hours or wearing and need to be removed due to rubbing on the foot.
A tip that many celebrities use is to take a second pair of shoes wherever they go for use when sitting down. High heels are then used for photo opportunities or when standing next to taller people only, reducing the ache that they can cause with prolonged use. This is a good idea for attending weddings and the like, where heels are best for the procession and ceremony, but not so good for celebrating or dancing afterward.
Being higher off the ground than usual can be useful for being on the same level as taller people, although falling from a height is much more painful. Because they are harder to balance in than flat shoes, high heels often cause a lot of accidental falls, particularly when combined with a slippery surface or alcohol.
The fact that they are hard to regain balance on is also a bad point about the design, as with flat shoes it is possible to regain your balance after a stumble. The impact of trying to regain footing suddenly in high heel is concentrated in a single point, meaning falling or twisting your ankle becomes much more likely. This is also what causes many people to snap heels off, as the heels can't stand the sudden pressure of someone falling onto them.
A less commonly recognized disadvantage of heels is that they are only suitable for solid ground, and can't be used on soft ground, in wet conditions or even on slick surfaces. Stiletto heels on soft grass will simply leave you impaled in the ground when you walk, and will make balancing even harder.
Similarly keeping upright on a highly polished floor such as marble or a tiled bathroom can be difficult. A night out can become a danger when it rains and you have to walk outside for a cab, where slippery wet pavements can lead to falling.
A common sight in many areas is drunken women falling down and damaging ankles and legs after drinking too much and then attempting to totter around too fast afterwards. While this still does happen in flat shoes, it tends to be much reduced, which is why women are a lot more likely to fall down than men when partying, due to men almost always wearing flat shoes.
Another disadvantage of high heeled shoes is that they simply don't last as long as flat shoes tend to because the heel either wears down quickly or breaks off. Heels can break off from falling, getting them caught in things like sewer grates or just from stepping awkwardly on them. The fact that the weight is focused on the heel rather than being dispersed throughout the whole sole of the shoe also means that the heels wear down a lot faster than other shoes would.
The last disadvantage of heels is that they can't be worn by everyone due to their height enhancing nature. Naturally tall people tend to look too tall and verging on the ridiculous when wearing high heels, and this often means that they miss out on large ranges of shoes simply because they are too tall for them.
It could be argued that being taller is its own advantage and that shoes don't really equal that up, but many styles of shoes are only made in heels and not in flats. Also certain occasions tend to demand heels of some kind, formal dances and the like, which makes choice of footwear difficult for taller people.