Introduction
The use of Chinese characters began in China's earliest history; artifacts known as oracle bones date back thousands of years, carved with older forms of extant characters and bearing witness to the history of the Chinese language. The characters have existed essentially unchanged for around two thousand years, since the invention of the small seal or xiaozhuan characters around 200 BCE.
Since that time, changes have been small, and though modern Chinese writing is only slightly older than Roman script, it has undergone fewer changes in the intervening millennia (that is, until the creation of the Simplified Chinese characters, which I will address momentarily). While both systems have demonstrated changes in form, the Roman alphabet has, during this period, doubled in size (adding lowercase characters) and added or imported many new characters as well: G, J, U, W, Y and Z. The oldest Latin texts were written with a mere 20 characters; more than two and a half times as many exist today (again, counting the lowercase letters) amongst the Romance languages. Because of its age, and because Chinese writing is non-alphabetic, it is sometimes characterized as anachronistic or primitive.
I intend in this writeup to explain why this is not the case. For several reasons, the Chinese writing system is uniquely suited to the Chinese languages; it has a place in the Chinese culture not only due to its elegance, beauty, and historical value but to its utility for the purpose of representing Chinese writing.
To understand their use, the basic structure of the characters must be understood. Most characters are composed of combinations of simpler characters. There are a small number of radicals that are combined to create a great number of characters. Many characters have a phonetic component which hints at the sound, and a radical to suggest the character's meaning. These hints are only that - it's impossible to determine a character's meaning or sound based upon them, but they do provide help in memorizing them. The pronunciations especially are questionable, as many words sound much different than they did 2,000 years ago.
The difficulties of the system
Most familiar systems of writing are alphabetic systems, in which characters representing sounds are strung together to express the phonetic quality of a word. They only represent meaning to the extent that related words have similar sounds. The Roman and Arabic alphabets, Cyrillic, Devanagari, their derivatives, and most other familiar scripts use this style. These scripts have few characters - the Roman alphabet has 26 in comparison to the 50,000 characters represented in one traditional Chinese dictionary.
Chinese, then, is hard to learn. Full literacy in the language, as defined by the Chinese government, requires learning 1,500 or 2,000 characters; learning enough to appreciate classic literature requires, according to some sources, twenty years of study. Why, then, is this system still used in a modern society? Certainly, in previous eras, literacy could be difficult, as scholars were members of a leisure class, and there was no need for the majority of the populace to read and write. But why has this difficult system survived to the present day?
The languages it represents
The Chinese languages - Mandarin, Wu, Min, Hakka, Cantonese, and others, along with their various dialects, are very similar in certain ways. They are all highly monosyllabic, and they all have a highly limited syllable structure. Mandarin syllables, for example, are composed of combinations of initials and finals, of which there are 21 and 36 respectively. These would seem to provide for a total of 756 possible syllables, except that many potential combinations of initial and final are not possible. Thus, there is a fairly small number of possible syllables in Mandarin.
The other Chinese languages tend towards more permissive syllable structures than Mandarin, but even so, they all have a far smaller syllable space than English or many of the Indo-European languages. Even the fact that Chinese is a tonal language, meaning that each word has an associated tone and thus that one syllable can represent multiple words, isn't enough to grant it a large syllable space.
The result of that is that all of the Chinese languages have an immense number of homophones, entirely different words, with unrelated meanings and separate histories, with the same pronunciation. For example:
試
識
十
帀
圅
是
示
室
all of which correspond to shì. Mind you, this is only a fraction: my small dictionary lists 25 different characters corresponding to this single syllable. This is only slightly more than most syllables have. (The characters are Unicode escape sequenced traditional Chinese characters. If you can't see them, you're not really missing out terribly.)
So why so many different characters for each syllable? Because these are different words, and in writing, it can easily be unclear or difficult to determine what word is referred to if only the pronunciation is given. Thus the characters, which let you know if you're talking about the number ten (十) or the word 'to be' (是).
So why is pronunciation enough to determine the word used in a spoken sentence, when in writing we need many separate characters? Because context is always much clearer in speech. Body language, the manner of speaking, and all the other nonverbal cues (prosody in linguistics) help. And the brain is simply much more up to the task of decoding speech - a natural ability with areas of the brain devoted to it - than of understanding writing, which isn't associated with particular brain centers.
And there's evidence for this. The Maoist government, during the 1950s, created the pinyin Romanization for Mandarin Chinese. Pinyin, probably the best of the transcription schemes in use, was actually developed in order to replace characters, in promotion of literacy. Yet native speakers find it difficult to read. Without the different characters, it's far more difficult. An alphabet, for Chinese, is simply quite impractical.
Okay, so characters are easier to read.
But wait! While that's the most powerful reason, there are still other aspects of the characters which make them useful. You see, the aforementioned Chinese languages, Mandarin, Wu, Cantonese, Shanghainese, and others, are all closely related. Enough that they are officially named 'dialects' by the Chinese government (although that is not accurate.) They all evolved from Middle Chinese, spoken around a thousand years ago, and written the same way.
A Mandarin speaker and a monolingual Cantonese speaker can perhaps work out some understanding, but only with difficulty. However, the two languages are similar enough that they can be written very similarly using characters. There are very few characters specific to one Chinese language, and the grammar of them is quite similar. Thus, a piece of writing is quite comprehensible to speakers of most of the Chinese languages.
By the same token, the characters are a link to the past. Chinese has a long, proud literary tradition. Literature dating back 2000 years can be read, with some difficulty to be sure, but with the aid of a dictionary, an educated Chinese of this century can read the writings of China's Golden Age, roughly a millennium and a half back. The same cannot be said of English, nor the Romance languages, nor, indeed, most languages.
In comparison, imagine that a system of logographic characters were used to write Latin (ignoring the difficulties presented by its highly inflecting grammar - no, it wouldn't really be possible, but this is a thought exercise). Given the grammatical similarities of the modern Romance languages, Latin and the modern Romance languages would be written the same way. A text in Italian would be legible to a French speaker, and ancient texts would be fairly accessible to modern readers. Such is the situation with Chinese.
The characters are also culturally significant. Calligraphy is often considered the finest of the fine arts in China; the elegance and beauty of the characters is obvious to anyone, Chinese-speaker or not. In earlier times, knowledge of calligraphy was de rigeur for any educated person; now it is less common, but still very much an art people take pride in. The beauty of the Chinese writing system is deliberate; it purposely reflects a Chinese aesthetic in a way that Roman characters do not.
A word on the simplified characters
Unfortunately, during the early years of the Communist government in China, the government took it upon itself to 'improve' the Chinese writing system by 'simplifying' many of them. In actuality, the simplifications were only a portion of the character set, and tended to apply to more complex, less-used characters, but it has made it difficult for those familiar with only one set to read texts written in the other. The 'simplification' did indeed result in syllables that are simpler in terms of the number of lines, and thus are perhaps faster to write by hand (although this is hard to address, as characters may be handwritten in 'cursive' scripts that generally have very few lines anyway). Simplified characters have not, however, shown any evidence of being simpler to learn. Linguistic data - the aforementioned suggestions of meaning and sound given in the characters, was often dropped. Some characters ended up looking much more similar to others. It's highly debatable whether the simplified characters produce any advantage at all.
Worse is the problem of communication between Chinese-speaking communities. While simplified characters are used in China, they are not used in Taiwan or Hong Kong. They are used in some nations with large Chinese-speaking populations, but most small overseas Chinese communities use traditional characters. And while newspapers and magazines almost always employ simplified characters in China, traditional ones are still widely used in books, as well as signs, and naturally for calligraphy. The result is that most Chinese citizens develop literacy at least in both character sets, although they may not be able to write in traditional characters.
Summary
I hope I've made clear the importance and usefulness of the Chinese script. It is old, and complicated, but 'anachronistic' it is not. I've even met a native speaker who professed his dislike of it - even after admitting that he couldn't read or write pinyin very well. Apparently he assumed that his knowledge of pinyin was insufficient - but it is more accurate to state that pinyin itself is insufficient to the problem of conveying Chinese. | 
