Alright, here goes. And yes, Merc, there are hundreds when you count all of the inflections on each word, but I'll list out the major categories...
Triconsonantal Root Systems, such as those used by the Semitic languages, consist of a collection of a few hundred roots (consisting of three consonants, as the name implies). When a certain vowel pattern is placed over these roots, a wide range of meanings can be assumed.
I've heard the system described almost like a multiplication table. On one axis is the root, and on the other is the pattern. Neither of these can stand alone, but when combined, their meanings mix.
To give an example of this, I'll use the root *K-T-V ("write").
If the pattern CoCeC (masc sg pres verb) is applied, it becomes kotev, meaning "I/You/He/She write(s)". The pattern CoCCim (masc pl pres verb) makes it kotvim "We/Y'all/They write". These exact same patterns can be applied to almost any root with the same result:
*CH-SH-V "think" > choshev "I/You/He think(s)"
*?-CH-L "eat" > 'ochel "I/You/He eat(s)"
*R-?-H "see" > ro'eh "I/You/He see(s)"
These roots also can form nouns and adjectives, given the right patterns. For example, maCCeC makes a verb into a tool:
*CH-SH-B "think" > machshev "computer" (lit. "thinking tool")
*P-T-CH "often" > mafteach "key" (lit. "opening tool"; p > f is normal lenition in Hebrew, and the additional /a/ is a normal phonological change before /X/)
The plural for nouns in the structure "CeCeC" is "CCaCim":
sefer "book" (from *S-P-R "tell, count") > sfarim "books"
seret "film" > sratim "films"
Some patterns can even be derived from other nouns. For example, the noun tochnah "software" has led to the development of the pattern "CoCCah", making a root into a piece of software:
*L-M-D "learn" > lomdah "educational software"
*G-N-V "steal" > gonvah "pirated software"
The list goes on and on.
For Mercator, here's all of the forms of K-T-B that I know of (there may be more). I don't list out the derivations of each, but I'll mention that they're there. Keep in mind that /b/ > /v/ allomorphic lenition is common in Hebrew:
kotev "write" (plus 25 other forms of the verb, in other tenses and conjugations)
ktivah "writing, cursive" (plus a dual and plural form, plus 10 singular possessive endings and 10 plural possessive endings; ie, +22 forms)
katuv "written" (plus a masculine plural, feminine singular, and feminine plural form; ie, +3 forms)
nichtav "be written" (plus 25 other forms of the verb...)
hikatvut "the act of being written" (plus 22 other noun forms)
mitkatev "correspond (+25)
hitkatvut "correspondence" (+22)
machtiv "dictate" (+25)
hachtavah "dictation" (+22)
muchtav "be dictated" (+22)
muchtav "dictated" (+3)
machetev "engrave" (+25)
ktav "text, piece of writing" (nowaydays these two are pronounced the same, but they didnt used to be)
ktuvah "marriage contract"
ktovet "address, inscription"
michtav "letter, note"
katav "journalist, reporter"
katavah "article (in a newspaper, magazine, etc)"
kitviyah "a collection of texts"
(Each of the above having 22 other forms)
There's certainly many more as well...
If anyone wants to calculate how many forms that is, be my guest!
Sometimes the adjective forms can be slightly idiomatic as well. For example, the root *G-D-L "to grow" yields the adjective gadol "big".
In foreign borrowings, roots can be extracted by pulling the vowels out of a word. For example, Hebrew borrowed the noun telefon from English. The root *T-L-P-N was extracted, and this can be used as a verb (eg, 'ani tilpanti otach means "I phoned you"). This is a rare four-consonant root. It functions the same as a triconsonantal one, as the middle two consonants are just treated as one.
Each of these patterns are productive. Even if a given word doesn't exist in the dictionary, you can just apply a given pattern to any root and you will be understand (just like how you can add "-ize" to many words in English, and you will be understood). For example, you could say telefoniyah, not something you'd find in a dictionary, but be understood as meaning "a collection of telephones".
EDIT: Actually, telefoniyah is a word. It's a telephony.
Next Up, Binyanim. And how they work in combination with triconsonantal roots.