As with most of my posts, this post is written on a whim. Specifically, I just happened to be talking with someone on an IM about this topic earlier today, and I had the whim to write a post about it.
There are four major types of writing systems: alphabets, abjads, syllabaries, and ideographic/logographic systems (those two are not the same thing, but for our purposes they're in the same category). You should be very familiar with alphabets. Alphabets are writing systems in which, more or less, each character corresponds to a single spoken sound, though the nature of language change makes it impossible for there to be a 1:1 relationship between sounds and letters indefinitely (some alphabets originally did have a 1:1 relationship). Some common examples are the Roman and Greek alphabets, Roman being perhaps the most widely used writing system in the world.
Next are the abjads. I believe I mentioned these a few posts ago. These are incomplete alphabets - that is, only some sounds (typically consonants) are written, and the rest are omitted. Sometimes additional characters may be represented by diacritic marks. Arabic, Hebrew, and Tengwar are examples of this. Arabic may, depending on the writer and the application, either omit short vowels (long vowels have characters just like consonants), or represent short vowels with diacritic marks (these marks are what give Arabic its distinctive glittery appearance, in cases where short vowels are written). Some writing systems may have an implied vowel after each consonant, and diacritics are only written when the vowel differs from the implied vowel; some may even have characters for all sounds, but omit some at the discretion of the writer.
Syllabaries, also mentioned previously, consist of one character for each syllable possible in the language (though they are also subject to loss of 1:1 correspondence due to language change). The syllabaries most familiar to me are the Japanese hiragana and katakana, although there are others.
Finally, we have a class that I don't know of a single name for, and include systems of ideographs and logographs. Logographs are when a single character represents an entire word - that is, there is a (near) 1:1 relationship between words and characters; the most well known logographic system, and the other contender for most used writing system in the world, is the Chinese writing system. Ideographs are similar, but in this case each character represents some idea or abstract concept. Contrary to common misconception, Chinese is not an ideographic system; however, the Japanese use of Chinese characters bears some resemblance to an ideographic system, where words frequently use multiple kanji (which is part of what makes the Japanese writing system harder than the Chinese system, as I mentioned in the distant past). For example, the Japanese word for goat (山羊) is written mountain (山) + sheep (羊).
Finally, there are complications/impurities in all of these. For example, some writing systems, such as Devanagari (an abjad with implied vowels), has one character for each consonant/syllable, but also has some characters which represent combinations of consonants/syllables; in other words, some characters may be combined to form entirely new compound characters in nontrivial ways.
Next post, resolve willing, I'll get to where I'm going with this (and why I've written this post so briefly and hastily - it's only background for the main topic).